To check if this is your issue, when the trackpad misbehaves (generally when on battery power) hold your finger on the shiny part of the VGA port, this will ground you to the chassis. While touching the port, if the trackpad now magically works, this is the fix for you, If not, you have other, deeper demons.
To do this, you need a small phillips screwdriver and a small piece of aluminum tape, generally salvageable from old laptops' EM shields.
Start by unplugging the power cable and removing the battery (use a pen(or srewdriver) to slide the slider lock to remove the battery).
The rest of the instructions are easier with the front of the machine facing you. Puncture the "warranty void if seal is broken" sticker. The phillips screw below the sticker is removed next. Once removed, use the rubber feet to slide the bottom plate off the machine. Remove bottom plate and set aside. This allows access to most of the guts of the machine, including the hard drive and RAM.
Cut down your aluminum tape to an approximately 1"x1/2" section and apply to the bottom on the nose as shown in the images. I terminated the tape right at the top case seam in order to avoid peeling and improve the aesthetics. The tape must reach the top of the rounded section to connect properly connect with the bottom EM shield(the shiny stuff on the inside of the bottom case). Trim the tape to match the top of the round section, and trim out the circle where the case screw lands (see pictures for details). Once this has been properly pressed down and trimmed, perform the disassembly instructions in reverse.
You now have a small contact patch that will ground you to the chassis of the machine, allowing you to kill static by intermittently touching it, or my preferred method of keeping my thumb in constant contact. Goodluck!
If anyone knows how to make the SD card slot work on battery power, please link it in the comments!