From what you describe the compressor is probably working just fine. I am more inclined toward a problem either with the fan motor its self or with the electrical power that supplies it. Do not try to solve this on your own, you need a pro to correctly diagnose which component has failed, but if you are describing it correctly then in all likelyhood it will not be a major repair (like a new compressor or a new unit!)
but outside unit makes a running noise like it's on. Also, it's 20 yrs old.
I'm guessing it's a compressor....time for a new system?
That's the problem....you're not alone, alot of people "guess". Have it checked out, could very easily be an inexpensive electrical part. Reversing valves make noise too on old units. At 20 yrs old, its done its job, and yes you will save $$$ on your power bill with a new one. How much, depends on alot of factors. Have it looked at, and then make your decision if its worth repairing. good luck.
If everything was always done "by the book"....the book would never change.