I've never heard of any cases where unplugging a monitor while powered on actually fries a video card or monitor. Otherwise, every KVM switch in the world would be frying monitors and video cards everywhere...
Now if he accidentally yanked the video card out of the PCI-e slot while it was powered on, then there might be a problem...
In this case, we're dealing with two separate problems: Internet and the video card.
First things first:
1) Turn off your computer!
2) Pull the power cord from the back of the power supply (just to be on the safe side)
3) Remove the video card and reseat it in the PCI-e slot.
4) Plug power cord back in
5) Turn computer back on (with monitor plugged into onboard video)
6) Use a friend's computer to download the drivers and save it to a flash drive.
7) Install drivers from flash drive. When asked to restart, say No.
Start -> Shut Down -> Shut Down in XP or Start Orb -> right arrow -> Shut Down in Vista. (not because of zapping hazard, but so the BIOS doesn't get corn-fused)
9) Plug monitor into video card.
10) Turn on computer. If you have picture, then you're done. If not, then keep going:
11) Turn off computer. Plug monitor back into motherboard.
12) Turn on computer.
13) Right-click on Desktop, left-click Properties (XP) or Personalize (Vista)
14) Go to the Settings tab (XP) or go to Display Settings (Vista).
15) You should now see numbers representing monitors. You may see three of them (one for onboard, two for card). Click on #2 and make that your main monitor.
16) Click Apply.
17) Unplug monitor from onboard and plug into card (this won't hurt anything unless you accidentally yank the card out of the slot).
18) Go into Device Manager and disable the onboard adapter.
19) Restart your computer.
20)
21) Hopefully Profit!