Not a dumb question at all. The stylus does not need to be charged, and has no battery within it. I forget the name for the technology behind it (crazy morning here at work, little sleep, no coffee) but it gets its energy from being in close proximity to the screen.
Assuming your normal touch functionality is working correctly, you could try re-installing the Digitizer drivers for your unit; I am assuming you have a tx2 series and not the older tx with the Wacom screen.
The likely cause however is that the pen itself is probably faulty. If you unit is still under warranty just contact HP and have them send you a new pen. If not, its only ~$20 for a replacement pen, so not too bad.
Moderator - Creator of Tx2 Touchsmart All in one Installer.
Touchsmart Tx2z Laptop: AMD ZM-87 CPU, 4gb Corsair DDR2 2x2gb, 256gb Corsair Performance SSD, Windows 7 Ultimate Signature Edition.
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