XPS 13 Typing, opening & closing windows on it's own.

My XPS 13 began typing & opening & closing windows on it's own yesterday. It also stopped recognizing my password. System restore did not work. I had a previous non-working touchpad issue taken care of in October, and not long after that my cursor started acting up by bouncing around while I was typing or deleting words on me. It didn't happen all the time, but often enough. Now that I am one month out of warranty, it went haywire. I took it to get looked at & it did the same thing for them. They were able to get the password to work, but all the problems occurred to the point where the repair guy asked if I had spilled anything on it (I didn't) or knew someone who would mess with it (no one has access to it but me). He hooked up an external keyboard, & the same problems occurred. No one could figure out what was causing the problems. He said it could be a software, hardware, or motherboard problem, or any combination therein (that narrows it down!). Can it be fixed? Would Dell extend the warranty to fix it or replace it if it is not fixable? Please help! Thanks!