There's something wrong with the clutch then. If it's in gear with the clutch pedal depressed, and it tries to move when you engage the starter, then the clutch isn't disengaging the engine from the transmission like it should.
Hopefully it's something with the clutch hydraulic system - the master, slave, lines... maybe it just needs to be bled. That's probably the easiest to fix.
Failing that, might be something with the fork that you can adjust with the transmission in the car.
Failing that, chances are you'll have to pull the transmission out so you can troubleshoot the clutch itself.