Before replacing the shift solenoid, I would check the circuit as best I could. It would be a shame to replace the solenoid only to find out that something had come unplugged or a broken wire was the cause.
These shift solenoid circuits are fairly straightforward DC circuits. Power is provided through the EEC relay, and the PCM acts as a ground side switch. I know I have detailed the test sequence somewhere on this forum. Basically, you hook up your meter to measure voltage drop across the solenoid. Run the "output state test" (see my notes on pulling EEC-IV codes thread or other description of this test protocol) and see if you can see the PCM energizing/de-energizing the circuit. Then a road test to see if the PCM is choosing to command the 3-4 shift. If the PCM never chooses or cannot command the 3-4 shift, then you can investigate the wiring and computer controls to understand why the PCM won't command the shift. If the PCM commands the shift, but the transmission does not respond, then you can look into the transmission to figure out why the transmission does not respond.