System Errors! Can anyone help please

The problem may be in the winzip drivers, but it's pretty certain that some of your system files are corrupted.

Now... if you were my client, here's what I'd do:
1) try to upload a file to a website (a known good file... something silly like a big text file). If it fails, then you have a major hardware problem and it's probably related to your clock chip (we would replace the motherboard. My recommendation to you would be to replace the whole computer.)

If the upload worked, then I'd go to Step 2:
Shut the computer down. Turn it on. Start hitting the F8 button (which interrupts the boot process.) Tell it to boot in "safe mode" and try copying a file to your A: drive (this would tell me if the problem was the zip driver or with your motherboard (a problem with the drive controllers.) I would copy several files onto a freshly formatted disk and would make sure that at least one file was a fairly large one.

If both those are fine, that means it's a software/DLL problem. The next step would be to go into the system setup (click on Control Panel, then System and look at the "hardware properties.") Check to make sure that you have the correct number of hard drives and floppy drives listed. When systems get horked, they often start by placing multiple definitions in the hardware listing. Knock out duplicates.

Turn computer off, and turn it back on (don't do a simple reboot. You want a full hardware reset.)

Try the file copying stuff again (don't interrupt the boot. We want a normal, regular boot.) If it's still horked then:

a) reinstall Windows
b) reinstall Zip software

If it's still horked, then you have to (oh goodie) install Windows into a new directory. This loses some of your old stuff and is a major pain.

The fourth option is to do a restore from a system backup that you know is good.