Are you using GTA version 1.0? Start singe player and see if theres a little text saying 1.01 or something. If thats the case, you will need to downgrade GTA.
Many people are complaining about the invalid serial number thing.
Heres the deal:
#1 - Register an account up here: http://mtabeta.com
#2 - Start the MTA installer and when the MTA Account page appears, select "I already have an account"
#3 - Fill out the account info from step 1 and it should be working!
it is not. Well, half i think. It is also because GTA freezes when you switch back to Windows. So when it is frozen no one is able to kill you etc.
There should be some sort of script debugging thing, like in SA:MP