Try what Ztcoracat just suggested to get logged in.
If that doesn't work, try booting in "recovery" mode, described here: Booting into recovery mode
If you get in with either method above, run the program that looks for proprietary drivers and install the Nvidia driver marked as "recommended". Not sure what program is called -- could be "Driver Manager" or "Additional Drivers", etc. If can't find, just type "Drivers" in Dash or application menu search box and it should return what you need. (I'm not that familiar with Unity, so not exactly sure of terminology.)
Reboot after Nvidia driver installed to see if that cleared up the login problem.
If no-go on above, post back with answers to following questions:
1. Have you tried choosing Windows XP from the grub menu?
2. If "yes", does it work to boot into Windows?
3. Did you do a test run of the live Ubuntu system before installing, or did you just start the installation as soon as it booted into the desktop?
4. Did you have the installer encrypt the disk or /home partition during install? (Doubtful since you didn't mention that, but can't hurt to make sure.)
5. Open a terminal and enter the following command, then copy/paste output back here for us to see:
I'm not sure what to think -- could just be the missing Nvidia driver. (We'll find out if able to get it installed.)
I would have thought possible keyboard recognition problem also, but if that were the case then even typing in the username wouldn't work -- which does right now, if I understand things right.
In Mint, which I'm more familiar with, there are times (for whatever reason) that grub doesn't get installed properly during installation. It's just a long-shot guess, but maybe that happened here too. (If it boots Windows, then probably not the problem.) If so, reinstalling grub from live DVD or running Boot-Repair utility
from live DVD will fix that.
Another guess (since this is an XP computer -- likely older machine) is that the specs of the computer are not up to handling the Unity desktop. Mint's Cinnamon desktop causes similar problems on lower spec systems, so that could be what's going on also.