Sounds like some other program running and eating resources. Go into task manager and check what's running and how much CPU it's using. That's the first thing to do in all cases of hiccups and unexplainable slowness.

But it's strange that a program doesn't run at all; that could be a problem with the video driver or video card. Did you check the settings (like the hardware accellerator)? Also run dxdiag (the directx diagnostic program from Microsoft). Or reinstall it in case it has been corrupted somehow.

And it's strange that ping speeds (to what site?) will vary. Of course, that's dependent on your ISP and connection speed, like an onlne game as SWG. So maybe your ISP has a problem, or cut down on your resources because you used your quantum for this month already (some do, if you don't pay for unlimited use). Did you already run a connection speed test?
Of course, with problems that only occur online, any regular Internet security program (like Norton or McAfee or Trend or Zonealarm) can be the cause. They do get updates once in a while.

Do you have a firewall to check your outgoing traffic? Set it to ask for all programs, and see if anything unknown pops up.

Also try a simple check on the connection: find a laptop somewhere and use it with your connection to do the same ping. Also do it elsewhere and compare.
You might also see if running the games (online games might not work) in Safe Mode makes a difference. Lots of background programs (including the really unwanted) don't run then.

Given that you did a system restore, I'm inclined to think it's an ISP problem primarily. Still, I don't exclude some unfound malware, nor a corrupted video driver (reinstall the latest one) or a hardware error in the video card.

The ultimate check would be to do a clean install of Windows XP (and all applications). But you might not like that.
- If things still are bad, it's definitely something outside your computer (so with your ISP) OR a hardware issue. You might need to bring your computer to a friend and use his broadband connection (with another ISP) to check on that part.
- If it is solved, it was some unknown sofware or setting inside.

Hope this helps and let us know.