I haven't taken the switch off to check for power or whether it's good. I don't have a voltage tester though. Do I need something like that to check for power?
What do you mean by "losing the neutral at the light"? I've re-wired and installed new switches and receptacles before, but that's about the extent of my electrical knowledge.
You can get one of the voltage tester pens for like $20.
You should have a hot wire and a switch leg connected to the switch, which are most likely black. You should have the neutral wires connected with a wire nut in the box, and they are more than likely white. The light fixture should be simple - white connected to white, black to black and copper to copper.
Like Gower noted above, you can get a power tester pen for cheap and check to see if you have power. If you have a hot wire, remember which one it is and turn off the breaker. Come back to the switch, check for power again to be safe, and check the connections at your switch and light. It's common that inexperienced people wire a switch or a light and they fail to properly secure the wires in the wire nut at the light and the wires in the switch. Check those first. Again, make sure you check for power when you are checking the connections at both the switch and fixture.
At the fixture, make sure the wires are properly connected in the wire nuts. Get a good connection, tape the bottoms off and make sure the wire nut opening is facing down when you pack them into the box to prevent water and debris from falling inside. Go to the switch and make you have a tight connection with the neutral wires. Tape that wire nut off and pack it into the box. Secure the proper lines, the hot and switch leg, to the switch and then tape around the switch for additional security.
Turn the power back on and try it again. If you still have an issue, it may be the actual switch. Just buy a new one and try it again. If it's still an issue, it may be the fixture.
And if it's a three-way switch, it gets a bit more complicated.
I realize it's cliche but safety first. If you're not used to doing electric work, make sure you aren't doing it after work when you are tired and out of it, and take your time.
Good luck.