Programs won't open

I got a virus about a month ago and I'm discovering various issues popping up from time to time since removing it.

I can't open most programs from the start menu or desktop icons about 90% of the time. If I reboot then sometimes I can run them but if the computer sits overnight and then I attempt to open the programs they won't open. It gives me the rotating blue circle like it's thinking about opening but nothing happens. Occasionally I get a window that says I don't have enough memory to open it but that's rare.

Downloaded, updated and ran the program and it found "Trojan.FakeAlert" so I removed it and rebooted and nothing is better. Prior to that I ran the Windows Repair CD and that didn't help. I don't want to do a clean install because I have programs on this computer that I don't want to lose. Any other suggestions?

EzioAuditore said:

Run sfc /scannow in an elevated command prompt.

SFC /SCANNOW Command - System File Checker

Follow this tutorial- DEP - Turn On or Off for Programs - Vista Forums
Make sure the first option 'Turn DEP on for essential windows services. . . .' is selected.
Reboot and see if it still persists.
If it does, run a memory test with MemTest86+ for atleast 6-8 passes.
Memtest86.com - Memory Diagnostic

I tried all of the above and still no success. Winzip, for example, will not open through any icon or shortcut, but if I download a .zip file and the process prompts me to open then Winzip will open. This is similar with other programs. I couldn't get to my Computer properties more than once after a reboot. Once accessed and closed, it would give me the rotating blue circle like it's thinking but won't do anything. In Safe mode, everything works fine, but once back in normal operating mode I get the same issues.