I have a 1997 Ford Ranger and I'm not sure if the alternator is charging the battery.

Get a volt meter and check what the voltage is at the battery

RIght, you don't remove the positive cable, too dangerous. Probe the battery with the cables connected and engine running, should be around 14V.

Tom is right. I had a customer that did what you did with the battery cable and he fried his ECM, Ignition module, and Radio. Hope you didn't already do damage. As far as the dieing problem, have you checked the fuel pressure?

It should be fairly easy to remove both battery and alternator if you have an autozone, oreilys, or advance type store nearby. They should also have a device that'll attach to your battery that'll be more helpful before taking those out to have them checked, and they usually check items for free. Removing the positive cable could short out if disconnected while running. Just don't forget to unhook battery if/when you remove the alternator or starter...

Thanks for the advice guys. Turns out my alternator was failing. Went to a Pull A Part and got one. Truck runs like a champ now.