What happened when you tried a system restore? Good info on System Restore can be found HERE
. An alternative way to use System Restore can be found HERE
Your computer is exhibiting signs of being infected. You could follow the directions in the HJT Preparation Guide found HERE
in an effort to clean it.
Find out what browsers will work on your banks web site, and download install and try a different one, such as firefox or opera (if they are supported by the site).
You could also try this: Start > Run > type " sfc /scannow " (without the quotes)
You might need your original XP disk that came with the computer. What will happen now will take a half hour or possibly longer as Windows will replace any missing or defective Windows files. When completed, remove the disk, reboot, and see if things improve.
In theory this will not affect your data or settings on your computer, but I would recommend backing up your data first anyway. Backups are never a bad idea.
If you run into problems with sfc /scannow, then you might look HERE
for an answer first. Or ask back here and we can help!
If none of those ideas work, then I would try a Repair install of Windows.