Two possibilities only.
1) A short to ground from pin 3 of the mike socket itself, or the tiny pc board behind it.
2) A short to ground INSIDE the CPU on the display board.
Follow the wire from pin 3 on the mike socket to the rear of the CPU/display board. Pull that plug.
If the TX indicator disappears, you have a short to ground on the mike socket.
If the TX indicator is still shown, this means the problem is INSIDE the CPU.
Can't get inside to fix that. And that chip is not available, even if you have the tools to replace a SMT chip with that many pins.
Most of these that I have seen were caused by one of two issues.
First is lightning, usually a strike to a power line near the structure where the radio is located. Had one customer that saw an arc jump from his landline phone to the D-104 on his 2527 when it struck the utility pole on the street. Caused this exact symptom.
Second cause I have seen is hooking up any sort of 12-Volt circuit to pin 3 of the mike socket. A relay to key your external amplifier, a noise toy running from 12 Volts, or any other boo-boo that feeds more than 5 Volts to the mike socket's keying wire.
The mike socket on this radio doesn't key the radio, it keys the computer. A wire coming out of the computer keys the transmit/receive switching circuit on the main pc board.
I have a really old Galaxy Turbo that I bought cheap because of this failure. In that case, someone removed the tiny DIP relay from the amplifier board, and installed a big "ice-cube" size relay from RatShack with long, unshielded wires that ran across the inside of the radio. To key it, one side of the relay's coil hooked to 13.5 Volts, and the other side to pin 3 of the mike socket. The 13.5 Volts feeding through the relay coil on receive zorched the computer's input pin where the mike's keying pin is connected. Showed this exact symptom. Recovered a used CPU board from a mobile radio and changed the connectors to match the base-station's wiring. Been using that radio on the bench for nearly 20 years now. And yes, it's the old one with the backup battery.
Sure makes me wish I had a few thousand bucks spare to design and make a batch of replacements for this family of radios. There are a lot of them out there with a bad CPU and no simple strategy to fix it.
73
