My power button doesn't work and I only see a white screen. The only way to reset the device I've seen is to hold the power and home button and then use restore on iTunes, but I can't do that for obvious reasons.
How could I reset my 4th gen iPod Touch just using my computer and a cable?
You might be able to use RecBoot. Here is some information quoted from their web site:
RecBoot is a free utility for Windows and Mac users which allow you to put your iPhone / iPod Touch in recovery mode easily. Its a great utility for for those iPhone users who's iPhone Home or Sleep/Wake button is not fully functional. Moreover this utility saves you from learning the 3-4 steps of putting your iPhone into recovery mode manually. Normally you need to put your iPhone into recovery mode when your want to do a firmware restore.
Once you put it in Recovery Mode, you see a popup on your computer screen saying "iTunes has detected an iPhone in recovery mode". From here, you should be able to restore.
Hold the home button until the phone displays the "Connect to iTunes" icon.
You won’t need the power button if you can let it discharge enough to turn on when it connects to power.
