Jump off and go in to find some ammo, along with a Bullsquid, a Barnacle, and some Headcrabs. Get back on the cart and keep moving. Around the next bend, a rocket launcher will begin firing at you. Strafe back and forth on the cart to avoid its fire. Take out the soldier just beyond the rocket launcher.
Blue lasers block the tunnel, so set the cart to a slower speed and jump off.
Follow behind it on the ledge next to the track. It will activate the lasers and you won't get hurt. Jump back on the cart when the path is clear. Jump off at the next area, which is teeming with Alien Slaves. Kill them all, and use the health dispenser.