... all temporary measures. I'm not an expert but you should be able to use the internet while in safe mode.
Get an updated virus scanner (you can even use a free one like AVG and avast! as those two have been the ones I've heard the most about), Hijackthis, and Spybot. Spybot isn't even really an antivirus program so with either Hijackthis or Spybot you'd have to be careful.
Turn off System Restore if you’re using Windows ME or XP. When you make changes to your system, Windows does a restoration checkpoint. If it does this while the system is infected, it may come back to re-infect later.
Restart the computer in Safe Mode. Since the Zafi.B worm creates running processes, and Windows doesn’t allow you to delete files connected with running processes, restarting is necessary. Using Safe mode prevents Windows from loading drivers and auto run entries so your system boots relatively clean. In addition, Zafi.B blocks the use of Regedit which is required below.
Run a full system scan with an updated antivirus scanner (or one of the online scanners mentioned above). If your scanner does not remove everything, follow the next few steps.
IMPORTANT: Your antivirus software should, during detection, produce a list of files associated with the W32/Zafi.B or W32/Erkez virus (depends on scanner). The files will be copies of the worm stored in the Windows system folder and shared folders mentioned above. You should set your antivirus to delete them. If not, delete them manually.
Make a backup of the registry before you edit. Delete the Run entries associated with Zafi.B from the registry. These will be:
HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Run
and delete the key:
“_Hazafibb”=”%system%\<random file name>.exe”
Also delete the key:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\_Hazafibb
Exit the registry editor.
Re-enable System Restore, reboot machine.
Re-scan to be sure all files are clean.
If you can I think to begin with you can at least use safe mode. Restart in Safe Mode with Networking. And you can try to use Trend Micro Housecall the online scanner.
Make sure to get a good antivirus software, even some free one can work well. Do be careful when using the internet (and don't install anything you don't know).