I took the cover off and watched it in action. When I insert a DVD, it starts spinning fine, then after about 10 seconds, it just plain stops. I am assuming it is some kind of motor or drive problem. Is it easily fixable by myself or do I just trash it and get a new one? I still have a VHS player along with it that works fine, and I hate to replace it as well. Any thoughts?
I doubt it's the motor since the disc spins, but more likely a problem with the laser pickup. You could try cleaning the laser lens to see if it's just accumulation of dust or debris. Other than that, I wouldn't say it's worth the effort to repair if it's broken.
If the VCR still works, keep it and use it as your VCR. Then, go purchase a stand-alone DVD player. A comparable unit will cost less than 100 dollars, but you may want to spend a little more if you want to get something that will last longer and offer better performance.