Question : I cannot open any webpage. AT ALL.

The network is working fine, other computers can navigate with no problem.
It pings, resolves names, but webpages simply will not load - seems to be timing out.
We've scanned it with Malware Bytes, two different antivirus - it did catch something, but pages will still no load after cleaning it.

ideas?

Answer : I cannot open any webpage. AT ALL.

The easiest way to do that is still with CSS and not with an imagemap. If you position text over the image, the color change is a snap.

If you insist on doing this with an imagemap, then scrathcyboy is most likely correct in that the internal Dreamweaver swap image behavior is not playing well with whichever version of IE is having the problem.  This is probably best solved by not using the behavior and searching for a different/newer one.