(link below) This is the Raymarine linear drive they have used for ages. If so, yes a new Raymarine course computer (or just about anyone elses) will interface to it easily. Chances are the fluxgate and rudder sensor would also be useable since Raymarine hasn't changed these in a long time either. Possibly even the control head (do you have a ST6000 Seatalk 1 head with separate course computer box? or the control head is the course computer?).
If you buy a new course computer from Raymarine, you probably want the X10 which will drive a type 1 12V linear drive, around $1200 from the discounters like Defender. It will come with a new fluxgate and rudder sense, I would swap these in since you have had problems with your old pilot why not? I think your old ST6000 head would work with it, if not a new one is around $500 more. If the old head is flaky or suspect, you may want to replace it anyway. For more money you can get the beautiful ST70 color display head, but it doesn't do anything fundamentally different. To interface to your Garmin, you need to get a NMEA 0183 cable (basically a twisted pair) from the Garmin NMEA output to the course computer NMEA input. Should work fine. I guarantee the X10 will steer the boat 100% better downwind than you are used to. Pay attention to the mounting orientation instructions, it is important to the solid state turn rate sensors.
The drive is a simple thing, two clutch wires and two drive wires. If it works but the course steered is wonky, then the drive is probably fine. There really isn't much in them, a DC motor, a solenoid clutch, some gears and a ball screw. It is easy to test if suspect. You will simply wire the 4 wires up to the appropriate terminals on the new course computer. With no drive to install this is a straightforward 30 minute job. Swapping the fluxgate and rudder sense are easy too, except for pulling the captive wire all the way through the boat.