You're right that the newer ones probably require more current - I hadn't thought about that. If the only thing keeping it from working was the connector then I think I could probably find a way to work around that. I am more worried about the mounting points and the gears. Looking at pictures on the Internet, I can tell that they are roughly the same size and shape, but it's hard to tell much more than that. I'll see if a local parts department has them in stock so I can look at them side by side.
I did think about the fact that it might not have been the motor's fault, and that a problem somewhere else might have caused it, but I'm not really sure how to go about figuring out whether or not that's the case.
This motor started getting weak around when the car had about 90,000 miles, and finally died right around 100,000 miles. I've owned the car since 45,000 miles and I roll the windows down a lot, as did the previous (second) owner. The front passenger side is also getting weak (it takes about a second longer to roll up than the others, and makes a slightly different noise), but it has been like that since long before the dead one started getting weak. The dead one died while I was in the middle of rolling that window up. About half way up it slowed to a stop and then wouldn't do anything. It sounded like it was trying, but the window wouldn't move. It had stopped like that a few times in the days before that, and each time started working again an hour or two later. This time it didn't. Not wanting the window to be stuck half open, I pulled the door panel off and connected the motor straight to the battery for a few seconds. It rolled the rest of the way up quite quickly. I tested the wires leading to it and they had 12 volts across them when the switch was pulled. When reconnected to the car, though, it didn't work at all and hasn't since. I don't know what those symptoms mean, but if anyone else does then that would be helpful. I wouldn't want to install a new one if it was just going to die again.