I have a comfortaire bhd501-d that is very noisy. Any solutions? I checked the screws on compressor and they are tight.

test fan turning freely doesnt mean much in way is diagnosis

I would guess that some rubber anti-vibration mounts have aged. If so this may allow the cooling fan to move and grate on the fan housing. It is unusual for the hermetic compressor to give trouble but having just said that, on rare occasions the big-end bearing can fail. This would cause a very obvious knocking noise coming from the compressor. Its just a case of carefully opening up the dehumidifier housing and looking to see what is happening. As an aide-memoire one can tape all the screws to a piece of cardboard adding notes as to where they came from. Take care and good luck!

Try pulling the grill off and see if the fan blade is rubbing on something. Check if anything else is loose while you have the cover off..

If you can hear its fan running but it produces no condensate, then it's apparent that either the compressor is not running, or that the humidity setting needs to be lowered. If the compressor simply won't start, then it's time to replace that unit. Compressor or controls repair is far too costly. It's best to put that money into a new dehumidifier. Frigidaire units are highly rated and that's what I would recommend as a replacement.

Place the dehumidifier feet on foam or rubber vibration absorbing pads.

Touch all sides of the cabinet with the compressor running to see if your touch will dampen the noise. Once the noisy area is identified check that the fasteners are all in place and tight. Sometimes loostening and retightening a number of fasterners around the noisy area will cure this problem.

replace it ...

Very expensive to replace a compressor. It is possible you blew a 'start capacitor'. This is not a cheap repair either.

I have a Comfortaire BHD501 dehumidifier. A couple weeks ago I noticed ice building up on top of the unit,so I unplugged it to defrost. I plugged it back in and it worked until I noticed the "CH" "01" code. It would run a few seconds then shut off with that code showing. I took off the front of the unit and noticed rust on some of the metal parts. Then I took the cover off the circuit board for the front read out. I noticed corrosion on some of the solder points. When I looked closer at the plastic cover for the circuit board I noticed a small burn mark. The water from the melting ice must have run behind the cover and shorted out the circuitboard. At this point I don't know if new boards are available.

I am still unsure here if your saying that the fan motor is running with the compressor or not? can you clear this up for me.

Yes, the fan motor should come on when you start the unit. 
I just came from my basement where i had the same problem.  My fan was not working- it was noisy at first, then it stopped working.  it seems the motor has some play in it and came out of the electromagnetic housing that should make it spin.  once it was slightly out , it no longer spinned.   I took it apart, and then reassembled it nice and tight.  there is still some play, but it is working great.  If it happens again i may try to get a replacement motor.