I recently had this problem trying to fix an old laptop running Windows XP Home. I found a solution here: http://www.pcmech.com/forum/showthread.php?t=139698 but I ran into a snag of my own when trying to run Task Manager.

The message Task Manager has been disabled by your administrator popped up when I tried to follow the guide. I suspect this is a curiosity of the XP Home disc, but it was easily fixed by running the Registry Editor and changing the appropriate flag.

The whole process is documented below for reference:

1. When stuck at 31/32 minutes, press SHIFT-F10 to bring up a command-prompt (yes, that one's news to me, too.)

2. Type taskmgr and press ENTER. If the Task Manager appears skip to step 3. If you get a warning, continue to 2a:

2a. Type regedit and press ENTER.

2b. Navigate to HKEY_CURRENT_USER \ Software \ Microsoft \ Windows \ CurrentVersion \ Policies \ System. You will see a value labeled DisableTaskMgr and its value will be set to 1. Double-click on it and change the value to 0.

2c. Close the Registry Editor and return to the Terminal window. Type taskmgr and the Task Manager should appear this time.

3. Look for the process(es) in the Processes tab that are hogging all the resources (ie, greater than 90% CPU, huge memory usage, etc.) and causing setup to freeze. If you don't see any, your setup may not have actually frozen yet. Patience, grasshopper!

4. Click "End Process" on each rogue process once you're sure they are causing problems. Setup should start making progress quickly after you've killed the right process.

5. Setup may freeze again at the 13 minute mark. If it does, simply repeat from step 1.

Do not be trigger-happy about loading Task Manager and killing processes. Ensure the that setup has frozen by waiting 30 minutes to 1 hour before acknowledging that yes, it really doesn't have 31/32/13 minutes to go!

Further reading: http://techtracer.com/2007/03/12/xp-installation-the-34-minute-hiccup/