I've been playing GTA III on Windows XP for a decade now...
There shouldn't be any problem. Make sure you have sp3 and have done all of your updates i use "slim drivers" program its the best. use that and make sure you have sp3. after that Re attempt.
In the Time of errors and all fails and you want another choice you could attempt to downgrade to v1.0 then upgrade to 1.1 and see if that fixes your problem first.
It should remove the issues of the steam version, if you do this Create a folder in the directory and name it Versions and copy and past the gta3.exe to keep yourself a backup in case something bad happens and you don't want to reinstall.
If Not show In this Forum STRONG Proof of purchase and ill send my gta3.exe v1.1
******if SugarD Agrees*********
And we will see if that fixes your problem.
But i must see your proof due to i don't condone piracy.Neither does the site, But we do want more Liberty Unleashed players.,.
This should automatically fix everything due to the steam.exe version has some weird blocking..
Hope to Hear Back.
and on SugarD's Message back on the mater of sending my version.