What video card and driver version are you using? Do please check the display properties for the display adapter on both XP Home and Professional and check if they're both using the same driver version.
Next check the refresh rates for the monitor and see if you or some other application has overridden the accepted defaults to a value that's not supported. This can sometimes cause problems and maybe when you change the monitor resolution, the monitor may be able to display the settings correctly without a graphics corruption at the same refresh rates. Refresh rates can vary according to resolution, and while some may be supported, others may not be.
What I am trying to say is that there is a "possibility" that the card may have been screwed up when the power surge and blackout happened. Is there another NIC around, or can you borrow a NIC from someone and then check it out? Or try removing the NIC from your system, removing all associated entries, and plug the NIC into another PCI slot and then reinstall it and then check it out there. Also if your NIC supports WOL, then check to see if its disabled in the BIOS, maybe that's causing the ACPI errors there on the list.
As for the other errors, well, this is what has happened. A Kernel Crash occured (1003) and it will restart from the bugcheck and save the memory dump (1001) to a file. I am guessing you would also have got a Stop Error with the code 0xC2. Its been known to happen when there is a sudden crash associated with the winsock handlers on the computer and is inevitably associated with a faulty kernel-mode device driver or device software tried to perform a memory operation incorrectly. So, there is all the possibility in the world that either your display driver or your LAN card is causing all the havoc you're seeing.
If you don't feel like reinstalling your OS, we could always run dumpchk.exe, install and run the Debugging Tools to examine the small memory dump files and then see what error code was generated for the 0xC2 error and then try to fix it. It won't be pretty or easy, but its the only way to avoid a reinstall. Frankly, if you ask me, a reinstall would be a HUGE timesaver in the situation.
And, oh, Windows XP Professional is as stable as Windows 2000 Professional, trust me on this. I've seen the MTBF values for Windows 2000 and XP and they're pretty much the same. Having said that, Windows 2000 Professional would be more tolerant on lower end systems than Windows XP Professional, so you might find that Windows 2000 Pro actually runs smoother and better than XP Pro on your computer.
As for Windows Server 2003 Standard, the minimum system requirements are met by your computer all right, but I wouldn't *dare* install it on any computer running less than a 1GHz processor and atleast 512 MB of RAM. And while you CAN use it as a desktop OS, it would be the same as using a Mercedes Benz to get to the shop at the corner of the road.