It is possible (with the syptoms you describe) that the transmitter's tuning is so far off (or has a fault) that it's causing abnormally high levels of RF within the case itself. This RF could affect the processor, producing the odd-ball behavior you describe and it would also explain the lack of range.

Can you swap the RF (frequency) module for another and check?

There are other potential explanations -- such as a cracked PCB trace or bad connection between the ROM daughter-board and the main processor board but unless you've had some experience and an anti-static work-area I wouldn't recommend DIY repairs.