There are a couple simple to repair things that can go wrong and cause those symptoms too. Can you look underneath where the motor is?
Hmmm, on second thought, it wouldn't agitate if the part I'm thinking is bad was bad... (depends on the model, it's a rubber piece on some of the Sears washers that transfers the power from the motor to everything else - it's the weakest link, thus the part that usually breaks (especially if you have a habit of overloading the washer), and it's an easy part to replace.
However, since it agitates, it's not that part. And, while other here suspect the pump, that wouldn't prevent it from spinning. I'd almost guarantee the problem is somewhere in the door switch or wire to the door switch. If the door is open, those are the two things that are supposed to stop. I doubt it's the timer.
If you've already abandoned hope, give the switch a shot - just eliminate the switch and connect the wires. I'm not positive if it's on a relay or not, so be careful - the wires may be low voltage, or they may be 110Volts.
edit: I hunted around and found two articles from a while apart.
here
According to that one, the timer (if it were the timer) is around $65 + shipping.
But, your symptoms are described better in this one (oddly, by the same guy 7 months after the timer was a problem)
here
Either way, if you're even slightly handy, I don't think it's too difficult or expensive of a problem to diagnose & repair. If you do decide to replace the washing machine, the motor probably has the most scrap value. Seems like they were around $1 per pound last time I was at the scrap yard, but I really can't remember for sure.