Cant get into programs

[#1]

I have a Sony Vaio laptop running XP and just managed to get rid of 3 nasties.
Stupidly I forgot top take note of what they were. I know that one was a trojan horse and the other two were worms
The problem they caused was making it impossible to get into programs
I couldnt run the antivirus program so to run a virus scan I took out the hard drive and ran the scan on my home computer using a caddy
The virus's are gone but the problems they caused remains
Whatever program I tried to get into I get the window saying "Open With" and a list of possible programs
It comes up with almost every program I try to open.
I tried System restore but it says that it is turned off.
Does that mean that I must re-install the whole operating system and each of the programs?
Or is there another way.
Thanks

[#2]

By The way. When I try to run System Restore I get the following message: "system restore has been turned off by group policy. To turn on Dystem Restore, contact your domain"

[#3]

I'm curious, Juliasdream, do you have some sort of sideline trying to fix computers or are you just very prone to problems?  If you're trying to do something professionally you really ought to learn how to fix problems like this.  If not, you are remarkable prone to getting yourself into trouble.
Obviously (?) the registry entry telling the computer how to deal with .exe files is corrupt or missing.  And there must be some other registry entry that has effectively disabled System Restore.  A little time and effort with a search engine will find solutions to these problems.  SuperAntiSpyware has some good blanket repair routines so they might be worth a try and you can download a .com version if you haven't yet found out how to cure your .exe problem.