I would definitely follow the advice about looking for a cause in the event viewer. But I think you also need to get a proper deployment method.
First I would install service pack 6 for VB6 so you are on the latest.
Then I would make a proper msi installer.
To do this you'll need:
Visual studio installer 1.1 from MS.
Merge modules for VB6 SP6.
The merge modules need to be extracted over the existing merge modules that come with visual studio installer and are found in C:\Program Files\Microsoft Visual Studio\COMMON\Tools\VSInst\BuildRes
Then I would create an msi installer and use that to deploy your app.
It will register the dlls for you and make sure the dependencies are installed.
To create an installer:
1) Open visual studio installer
2) Pick the VB Installer package type in the wizard
3) Change the name to the name of your project
4) Change the location to where you want the installer package to be created (I typically create a folder under the project called Install)
5) Choose create Installer, not merge module (unless you want to package up dependencies for a subproject)
6) Pick the existing VB project to deploy
7) Under Files on right add any other files that aren't straight dependencies (documentation or other related files)
8) Under Build Menu -> Build Configuration change it to release.
9) Click File System, then Application Folder, change the default install folder to be <company name>\<app Name>
10) Right click and Delete unneeded/bad dependencies. For example MDAC.msm doesn't normally need to be deployed by the app.
11) Change ActiveX dlls to be self register in properties.
12) Under File System, User's Start Menu - Add folder hierarchy User's Start Menu -> Programs -> <company name> -> <app name>
13) Drag system created shortcut to app from User's Start Menu to the App Name folder. Rename as appropriate.
14) Add shortcut to user's desktop folder if desired
15) Add any other file shortcuts (say to documentation) in the App Name folder or user's desktop
16) Under User Interface, click all the leaf nodes (like the welcome screen) and change the banner bitmap if you have one.
17) Configure Project Properties as appropriate (I fill in support information and update version number)
Build -> Build
THe msi file will be created in a subfolder of the install folder.
Whenever you make a new exe you just open the existing visual studio installer project and choose build->build. It will create a new msi for you.