Anybody know of a service/company that would host a web application that I want to build from scratch, where I may have access to some admin function of the web server and J2EE server, and database?
I'm looking to build a site that is public to show off my skills when applying for a job.
I don't know of any free service that allows you admin access.
But if you are willing to pay for this, then there are tons of options. Just search for 'vps hosting' on Google and go with a provider of your liking.
With VPS hosting you will get 'root' access and your own virtual server to play around with and do as you please.
I'd also look into building/hosting your own server. If you're on a dynamic IP, there are plenty of free services to provide a hostname - and others allow you to use your own domain for a fee. Not only would you gain experience in building your web app, but you'd also have skills in setup and hosting.
There's always the free option of running your own server, which has the side benefit of providing you with all sorts of admin experience, and the ultimate in server choice. Or for an all-in-one solution, rather than hand-picking your servers, you could look at XAMPP. (Note that XAMPP does require some hardening of the security settings from the base installation if you want to use it as more than a development/test system.)
Another possibility -- deploy your software in a virtual machine and let your clients download a playable VM image to mess around with it. This also shows that you know how to configure and administer a DB/J2EE server, and you can concentrate on writing software instead of finding a hosting provider which will let you do the things you want to their systems.
Also, and I of course mean no offense here, but I get the impression that you may not be so skilled in administering your own servers. If this is the case, then working in a VM is also a handy way to learn about this kind of stuff without the risk of messing up your actual workstation.
Check out http://www.stax.net - they're taking beta users. The basic tier is free, at least during the beta. I tried them out and they work great.
Another option (not free but pretty cheap) is to use Amazon Elastic Cloud. You can create your own Virtual Server (Windows or Linux) and make your own image by placing everything you need on your server. I'm using it and it's pretty easy to use and affordable.
You might be interested by these related questions:
Which J2EE Web App Hosting Would You Recommend for Casual Projects?