RCA TV is haunted?

Unfortunately, I do not know the model number. It's an RCA TruFlat CRT 27" model.

I sat at my computer last night, and suddenly my TV turned on by itself, began changing channels (from CMPT input), finally settled on CH 02. Then the volume started going up on its own, all the way to max (100). The remote is more or less unresponsive. The buttons on the front of the set do not work, except for the Menu button. After I've pressed the menu button, the buttons will work, but the volume (and so any setting I happen to be on) still tries to go to maximum.

I've tried cycling the memory by unplugging it for several minutes, then plugging it back in, but the problem remains. I did, however, leave it unplugged overnight. When I plugged it back in, I was able to gain a few seconds of normal operation with the remote, and got it to change back to CMPT input and turned it off. I then took a shower, and when I got back, the TV had turned itself back on again, was on CH 02 with the volume at 100.

This is vexing.