I can actually get it to the HTC logo screen and then it turns off. This happens with the charger connected, and without. I can also get it to the boot screen, but if I select anything, when I press the power button, nothing happens. I've also only seen the red charging light a couple of times, but not recently. I've already ordered a new phone, but still hoping to salvage this phone as pictures weren't backed up.
Plug the charger in and leave it alone for 4 hours. If it doesn't come on longer than before, the battery is shot. (Plugging in the charger with a totally dead battery won't do any good - it takes at least half an hour before the battery starts charging, and during that time there's not enough power available to run the phone. (Considering that the phone is over 6 years old, it would be no surprise if the battery is pretty dead.)
The fact though that it does power on to the logo screen or the boot screen shows that the battery must be working somewhat, right? I really just want to backup the pictures and then it can become trash. Is that even possible?