I have a Kenmore, model 10502 990 top loader, type 110. The year it was installed was 2001. It works well, but the washer's spin cycle does not get out sufficient water from the clothing.
The average working life for a top loading washer is about 14 years so your washer is well beyond the average. The possibility of fixing the washer yourself versus a repair service may be moot at this point. We had a similar aged washer needing repairs recently so called in a service; the repair tech said it would cost more to fix than to buy a new machine. So we bought a new machine that performs well and the new machine's technical advantages are a "new world" after our old and basic 15 year old model!
I think it depends on the cost of repair services in your community. I have a similarly aged machine, and a few years ago the spin cycle quit working. At that time, our local repair person popped over, fixed the machine in less than 30 minutes, as it is a very common problem, and I have been washing merrily ever since. The bill was less than $100, including the new part. As well, a few weeks later, it happened again, and the fellow repaired it again, free of charge, as he said it should have lasted longer! If you have such a repair person, call them in. My fellow was able to diagnose the problem over the phone.