I think your first step should be to buy a replacement battery as it sounds like your charger is still working. Here is a link to the battery replacement guide: Lenovo ThinkPad T500 Battery Replacement And if anything else pops up, here is the link to the general troubleshooting page: Lenovo ThinkPad T500 Troubleshooting
Users have had trouble with this same area as well. I would suggest pressing the middle mouse button before using the trackpad to scroll with. When using the middle mouse button, your trackpoint will not be able to move until you let go of the button, so make sure to scroll with the trackpad.
not action shots
not an action shot, no markups
not an action shot
no markup, second picture is blurry
potentially wrong tool, it is easy to scrape the screen with a metal tool
not action shot
not and action shot, shadow shot, and then another still frame
not an action shot
redundant pictures
Don't touch the RAM unless grounded or you can ruin it