Companies such as Blizzard typically require a 4-year degree in computer science or equivalent for their entry level game programming positions. It is likely your best bet (and widest range of career options down the road) will be to transfer to a 4-year school and get a Bachelor's in Computer Science.
Typically if you have built a demo on your own time, that helps get you a job over the other 4-year candidates. Are you familiar with Gamasutra or Gamedev? They will be a good help for you.
edit: also, there's a lot out there besides programming in the game industry. Game designing, art, public relations, etc.
edit2: Building a game from scratch means building all the code yourself from DirectX on up and not using (ie) the Unreal engine or other engines - you design the engine.
edit3:
To sample some of the top game company hiring practices, what they are looking for today, April 2, 2010, I went and grabbed some jobs from EA, Bungee, Lucasarts, and Blizzard for some current game dev positions, finding what appeared to be the least-qualified programming position, because you would be starting there right out of college (presumably).
Summarized, the commonalities of what these companies look for is experience, passion for games, strong math and algorithm skills, and strong C++ or Java.
For experience, your game-dev AS will provide some of that. University coursework almost as a rule isn't like a real product.
Passion for games, no one can teach you.
Strong theoretical skills, you will probably need from a formal education. In my opinion, that's the best technical benefit from formal education; the theoretical knowledge that is centered there.
Strong C++/Java - some of that comes from formal education, most of that comes from your personal projects and study.
Most other nuts-and-bolts knowledge can be absorbed on your own time. The abstract end of software engineering, artificial intelligence - not game AI, but the broader field which game AI comes from -, computer organization/architecture, operating system theories, etc, those typically are impossible to find at Hastings or Barnes and Nobles. You will probably not find that information in an AS degree. You will hopefully find it in a BS degree to some degree. In a good BS program, it will have a MS/PhD program as well, and that will dramatically increase the academic culture to a quality untouchable by other schools (experience speaking here. -.-).
I also want to point out the communication ability these jobs look for. It is worth people's while to take some soft and gooshy humanities courses to work on communication skills, especially communication to those notoriously ambiguous non-programmers. :)
EA
This is the least stringent of the requirements of the jobs I glanced at - the only one that didn't say 4-year degree up front:
Primary Responsibilities:
•Development of new games and related features
•Contribute to the evolvement of our existing games
•Maintain detailed design documentation throughout the project cycle
Key Requirements:
•Strong programming knowledge across several languages and platforms including ActionScript 3, Java and/or C++.
•Solid understanding of algorithms, physics and math.
•A natural feeling for and understanding of good gameplay mechanics.
•A wish to learn and share knowledge and experience with other team members.
•Someone who is open for input and enjoys working in an iterative and agile process.
•Specific Flash/AS3 knowledge is a plus.
•Relevant game development and/or demo-scene experience is a plus.
•Most important of all, you need to love games!
Desired:
•Experience in relevant game development and/or demo-scene
•Computer Science degree or related discipline
Bungee
Of the two jobs listed at the moment, this one did not require a 4-year degree. The other one did.
GUI Engineer
Bungee Labs, an Orem, Utah based company, is looking for an experienced GUI developer to be part of the design, development and release of a next-generation service platform as a Service (PaaS) offering. The candidate will be working within a highly talented motivated team of fellow software engineers. Bungee employees are well rewarded for their expertise, drive, initiative, accomplishments and teamwork.
Requirements
Experience building GUI tools
Experience writing GUI software
Experience building custom controls
Proficient in C++ and / or Java
Experience building Web programs
Minimum 5 years of experience
Blizzard ##
Blizzard typically requires 4-year degree or equivalent (I've watched their jobs page for a few years now off and on).
This is the 'associate sw engineer' position, which is the entry-level developer.
Associate Software Engineer
Team: Next-Gen MMO
Blizzard Entertainment is looking for a talented and enthusiastic software engineer to work on its next-generation massively multiplayer game. This position is for a software engineer who will focus on network communication and database design and implementation.
Requirements
Strong C/C++ programming Skills
Familiarity with implementing client/server architecture
Excellent spoken and written communication skills
A passion for games
Pluses
Networking experience in TCP/IP and UDP protocols
Fluency in procedural SQL programming (MySQL, PL/SQL)
Familiarity with relational database architectures
Experience with code optimization
MMORPG Gaming Experience
BS or MS in computer science, mathematics or equivalent experience
Code samples are required. Please include samples of your work along with your resume and cover letter.
Job Status: Full-time Permanent
LucasArts
There didn't seem to be a low-end position open.
The Network Engineer focuses on multiplayer game programming for Xbox360 & PS3.
Provide technical expertise in network game development and technologies in support of our game development cycle.
Reliably create good quality, performance-minded code.
Provide a complete task list and schedule for responsible work. These should be complete and accurate. Assist less experienced engineers with the creation of their task lists and schedules. Inform others when the schedule is at risk.
Assist in the sharing of ideas and exploration of new practices to continually improve the quality of game development within the Company.
Provide leadership and insight to help the team avoid and overcome obstacles as they arise during development.
Provide coaching skills to help develop less experienced engineers.
Maintain a professional attitude during all stages of development.
Excel as a team member and strive to maximize team and departmental performance.
Requirements
B.Sc. Degree in Computer Science preferred, or equivalent game experience.
3+ years experience in the area of Network Engineering & Multiplayer engineering specifically for console games.
Prior programming experience on xbox360 or PS3 is a must.
Broad understanding of computer and game networking systems, including DNS, NAT, firewall, security methods, peer-to-peer and client server models.
strong C++ programming skills/experience required.
Shipped at least one title on the target consoles.
Ability to work independently and to be self-directing required.
Excellent team and communication skills required.
Passion for making and playing innovative games.