Could also be the power supply, which would cost more than that telly's worth. Pick up another CRT off Ebay if you don't want to drop the cash on a flatscreen or fix it. I picked up a Panasonic 32" CRT for £70, and you'd be hard pressed to get yours fixed for less.
As for why not... TVs have some very, very high voltage equipment in them that don't discharge just because it's off and unplugged. I've seen someone thrown across a room by touching the wrong bit.