Firstly you need to read
the support statement for VB6 under Windows 7[
^] - this will hopefully explain why a program that works on XP will not necessarily just run on Win7
Next, problems with msadodc.ocx are common - e.g.
this thread discusses them [
^] and there are several more via google.
Win7 Service Pack 1 caused many issues, so make sure your Windows Updates are up to date.
Finally, I'm currently working on a project to migrate some VB5/VB6 programs onto Win7 and I'm wishing that a bite-the-bullet approach of converting to .NET was an option. If you have that option then go for it!