Windows Backup Software

i have a windows vista laptop. i have microsoft office and photoshop on there. I for some reason have trojans have on there. i thought it was from a couple little files i had downloaded. i deleted those files. but the trojans are still there. i tried running an antivirus software and it didnt work. i want to try a system recovery, but i will lose those files. is there anyway i can back them up without losing the serial numbers for them?

i mean like can i back them up without having to buy them again?

If you paid for them already you should have the CD and SN already right?

You can’t really back up software programs because they need to be installed for your computer.
You can do an image of your hard drive (which backs up everything) but that would probably keep the virus also.