Sorry to hear that you're not able to use the Mac App Store.
There are a few articles that can walk you through troubleshooting:
Troubleshooting the Mac App Store
Mac App Store: Sign in sheet does not appear, or does not accept typed text
Mac App Store: Solve problems
I would look through them in that order, and see if those solve the issue.
I recently developed a problem with the App Store sign-in sheet. Whenever I tried to enter my password, I'd get trapped in a loop with my password never being accepted.
I tried a TechTool pro File Structure test and it flagged "com.applestore.plist" as (Unexpected character c at line 1)
I went to Users/Username/Library/Cookies/ and deleted "com.applestore.plist"
I also discovered a file "Cookies.binarycookies corrupt." Deleted that as well, as there was a clean version of it there.
I'm now able to log into App Store, view my account information, download updates, as well as view Purchases.
This is in OSX 10.8.4, so not sure if it applies to Snow Leopard.