I've personally fixed a lot of Partner modules, both processors and line card modules.
One of the other posts was correct in that some of the 206 modules contain their own processor, and so these are capable of some "basic" functions all by themselves, without needing a separate processor module. In other words, one of these 206 modules all by itself will work as a very small system (2 trunks, 6 stations).
Now, for the noise issues:
Each partner system module has its own built-in AC power supply. Because these are located at the top of each module and the cooling is very poor due to the thick plastic housing, these power supplies run HOT.
As a result, the electrolytic capacitors in them dry out. Once this has happened, either there will be a lot of noise (often a "hissing" noise) or the module won't work at all. When the power supply is the source of the problem, there will be a hissing noise in ALL of the station ports.
Repairing the partner modules usually consists of locating and replacing about 5 or 6 electrolytic capacitors in the power supply. Any electronic technician who fixes computer monitors or DVD players is probably familiar with "dried out" electrolytic capacitors. This is one of the most common failures in AC power supplies.
Also check the large circuit card in the 206 modules. There is a row of medium sized electrolytic capacitors in the area of the 6 station ports. Sometimes these leak electrolyte all over the large circuit board. This causes one or two of the station ports to have crackling noises or to completely stop working. Cleaning the circuit board and replacing the leaky capacitors often solves this problem.
Since the power supply runs directly on AC power, replacing the electrolytic capacitors is only recommended for those who are skilled in general electronic repair and PC board level unsoldering and soldering. But the cost of the 5 or 6 capacitors is probably under $10.00. These are readily available from places like Digi-Key.
Some of the Partner modules also contain a nicad "backup" battery. These allow the system to retain all the installed settings during power failures. Often these batteries go bad. If your Partner system loses all of the programmed settings after every brief power interruption, then the battery is bad. The battery is soldered in, so again some electronic technician skills are required for a "do it yourself" fix. Note that this battery is NOT intended for "long term" backup. Losing power for more than about 24-48 hours will result in loss of all the programmed settings even if the battery is good.