I have a 1990 Honda Accord DX with automatic transmission. I only recently got the car, and it had this issue when I got it. I will do my best to explain the issue.
All forward gears, park, and neutral work as you would expect. When trying to shift from Park to Reverse, it takes a bit of muscle to get it to go. It's stiff, essentially. If you leave it in reverse, the car makes this horrendous grinding noise and doesn't move. Every other gear works fine, as expected from a working transmission.
I'm going to try replacing the fluid soon, and was wondering if this might be a solenoid issue? The car has high miles, 250k+. As far as I know it's original motor and transmission.

 

Friendly bump.

 

Drain the fluid and drop the pan. Look and see if the fluid is dark red (black) or smells burnt and whether or not there are pieces of metal shavings in the fluid/pan.

Hate to say it, but it sounds like you are going to need more than just a fluid change or solenoid replacement though.

 

Hello,
We have a 1990 Honda accord that is doing everything you described in your post. Everything shifts fine except sometimes when you put it into reverse it makes a grinding noise as if it does not want engage reverse. Sometimes it will engage. Can you tell us how you resolved your problem? Thanks Steve

 

Can you tell us how you fixed the problem? Our 1990 Honda Accord is doing the same problem you described. Thanks