I had the exact same problem. Trying the .iso or .dmg install options mentioned elsewhere did not work for me.
What DID work was this solution:
http://kb.parallels.com/entry/31/280/
Even though the title of that refers to XP with SP0, it's also a problem with SP1.
When it gets to the spot where it's hanging, press the VM Stop button, answer yes. Then after the window spins around, click on Configuration (or choose it from the menu) and choose the Advanced tab, set the Acceleration Level to Disabled. Then restart the VM, it will restart the installation and...it worked perfectly for me!
Once windows has finished launching, you can Exit windows (shut down), go back into configuration, and set the Acceleration back to High.
Note: I have a Dell XP SP1 install disk, that was not the problem.
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