[COLOR="Blue"]The motor attached to the dispenser makes a very loud rattling sound.[/COLOR]
There is no motor on the dispenser, it is run by a solenoid.
Was this what the old dispenser was doing?

[COLOR="Blue"]How do I correct it?[/COLOR]
I am assuming that the rattling only occurs when the dispenser is trying to open (relay chatter).
Remove the dispenser and check that you can activated it manually, just in case it is a mechanical problem.
You could check the solenoid winding for resistance, should be 280 to 340 ohms.

The best way to check it is to hook it up to a line cord, then plug the line cord in to see if the solenoid will open the dispenser properly. This is also a dangerous method so be care full that the line cord wires cannot short to each other and you do not get a shock.
If it works OK here then I would suspect the control board re: triac.

The solenoid is run by a triac on the control board. A triac is a solid state device that passes AC current when triggered. If the triac blows it can pass only half the 120 volt AC so you end up with about 60 volts AC feeding the solenoid. This is not enough to pull the solenoid in properly and you get chatter.

Could be you received a defective replacement.
I would suspect this if the original problem was different.

[COLOR="Blue"]Do I need to replace the who control board?[/COLOR]
In most cases the answer is yes.

Personally I would trace back the wires / board trails to the correct part and then replace that triac.
With luck the triac will have manufacturer's numbers on it so you can get a replacement from an electronics supply house.
You will need some de-soldering and soldering knowledge.

The above is a gamble as it could be that IC that controls the triac is not working correctly but worth the risk due to the difference in cost.
You would need an Oscope to fully troubleshoot down to component level.