First, DirectX 10 is Vista-only, unless something happened in the three months I've been gone to change that. If you're on XP, you should have DirectX 9.0c installed (as your System Restore indicates).
Second, you should only need to reboot _once_ to get back to Windows. If it locks up, just hold down the power button on your PC tower for ~4 seconds, and it'll turn off. Wait a few seconds, then turn it on normally. Can't see why it'd take more than a single cycle to get back up.
Third, is the graphics card overheating? If you've not done so in awhile, try opening your case up and taking a can of compressed air to it while the PC's off. Or have someone else do this for you, if you feel uncomfortable with doing so. It would seem odd to start happening after Age of Empires 3 got installed, but you can never be sure, these days.
Fourth, run any security and maintenance programs you might be using (antivirus, defrag, disk cleaning, etc) to see if that helps remedy the issue--could've gotten a virus you don't know about.
As to debugging this problem, you should never trust System Restore to fix things for you. That said:
Try uninstalling Age of Empires 3 foremost, reboot your PC, and try to run an older game you
know worked before. If that works, swell--try reinstalling AoE3 and see if it decides to behave.
If that fails, then you might want to try finding out the version of your video card drivers. To do so:
- hit Start, then Run, and type in sysdm.cpl--hit Enter once it's in there.
- In this new window, click on Hardware, then Device Manager.
- In here, hit the [+] next to "Display Adapters" and right-click your graphics card, selecting Properties.
- Click the Driver tab, and give us the "Driver version" it reports.
Reason I ask for this is that someone might be able to shed more light on the issue (and we can see if your drivers need an upgrade). Unfortunately though, I'm way out of practice, so I can't help you more than the above advice. Sorry!
Jam it back in, in the dark.