Hi @toneman ,
Given that it has been idle for a few years, try replacing the non rechargeable CMOS coin cell battery with a new one, (they usually have a life span of 5-7 years and its’ most likely depleted) and then see if it starts OK. Removing the battery also has the effect of resetting the BIOS back to its’ factory default settings which may help if there were any corrupted settings preventing correct startup.
I realize that you said that you have a Touchsmart 320 but here’s a close up image of the battery, taken from the ifixit HP Touchsmart 300 Removing back panel and components to to get to CPU guide at Step.13 (also seen in Steps.11-12). Hopefully your model is not too much different as to the battery or its location and the guide will be of some help to you to gain access to the battery in your model.
(click on image to enlarge for better viewing).
Also, try using a USB keyboard and/or mouse to see if that works for you to navigate through the PC.