The Throttle Position Sensor basically tells the computer how far the throttle is opened so it can adjust the fuel delivered by the injectors properly. It is one of several critical sensors the ECU uses to maintain the air/fuel ratio close to ideal. You are bypassing that function by supplying the fuel via starting fluid, so you need to test the TPS.

There are lots of vacuum lines that control many things. The fact that it runs on starting fluid only tells you that the engine isn't getting a rich enough fuel mixture to run. A leaking vacuum line can let extra (unmeasure by the AFM) air into the intake stream, which would lean the mixture. Not to mention that whatever device that line is supposed to control to isn't doing it's job, either.