Windows 7 Network and Sharing Center crashes Explorer

This problem has been going on for around two weeks, but I'm not entirely sure if all the symptoms are related.
My computer is around four years old, but has never had any major problems, though I did reinstall Windows at some point.
The problem only seems to start after Windows has been running for awhile. I'll admit, I have the slight flaw of leaving my computer on for very long periods, but there doesn't seem to be a exact threshold at which this problem occurs.
The first sign I usually notice is that certain programs won't open properly. They show up under the processes section of Task Manager, but don't actually show up in any visible manner. These programs run the gamut from DivX Player, any Chromium browser, to Batman: Arkham City. The only thing that seems to connect these programs seems to be that they all access the Internet in some manner. Once I noticed this, I attempted to open Network and Sharing Center. After a short period, Explorer crashes. Icons, task bar, everything but the wallpaper disappears for a second, then reappears. After this, the network icon does not show in the system tray, and connecting to the Internet seems impossible. At any point after the initial signs show, attempts at restarting or shutting down results in the computer hanging at the words "Logging Off" during the shutdown sequence and the only way to proceed is to hold down the power button until it forcibly powers off. I'm quite frankly stuck on what to do next.

Have you tried System Restore to a date before two weeks ago? You may have to click a line to show more System Restore points. Start, All Programs, Accessories, System Tools.

Berton said:

Have you tried System Restore to a date before two weeks ago? You may have to click a line to show more System Restore points. Start, All Programs, Accessories, System Tools.

I've tried that, and even with Show More Restore Points, it doesn't show any points from before I tried it. It acted like System Restore wasn't "on" beforehand. If that is the case, I'm kicking myself for not remembering to activate it. There isn't anything in terms of personal files that I didn't already have backed up, so if all else fails, I can just do a clean install, which will be a task in itself, as the Recovery Partition has never worked, and Dell doesn't ship restore disks with purchase anymore. I posted here because reinstall is really a last resort. Thank you for your advice, though.