I don't know exactly but there is a whole discussion on that here :
Brother HL-5140 paper jam

Also there are some parts that wear out - see page 105 of the manual.

Brother HL-5140 Manual (pdf)

Paper jams usually are unrelated to the PC sending the print job.

If you can't sort out the problem yourself, it wouldn't be worthwhile to pay for a repair because these units are inexpensive. Be comforted in knowing that you can probably buy a replacement today with more features for less money than you paid years ago for the Brother.

Unless you need a higher volume or speed performance, you should be able to find personal black/white laser printer-only models for under $75, and very good Brother - Canon-etc combo units with scan, copy, fax and print functions for under $100.

Audrey, Does the Red light Blink in any certain combination of Flashes. Kinda' like Morse Code, the Flashes mean something. Each printer is different as well as each manufacturer. I have 4 Brother Printers, 2 Color Laser AIO Machines, 1 Inkjet AIO and a Label Printer. Right now I have one of the Color Lasers on the fritz. These have Readouts and don't have blinking lights, but they both serve the same purpose. Check the number of Flashes and then check the Troubleshooting section of your manual, it should give you a better idea of what might be wrong. Mine tells me that I have a Paper Jam, I've torn it apart and can't even find a little corner of a piece of paper in there.

Check for miniscule pieces of paper or even large dust near the sensors in the paper path. You'll need to check the manual for the location of the sensors. Once you've cleared every possibility of paper, no matter how tiny, power it down and unplug it for a minute. Sometimes that clears the error. There may even be some key press combo to clear the error, but again, you'll need the manual.

Thanks, everybody, for the input. No, the red light doesn't blink in any particular pattern. It just blinks. I've already checked for little bits of paper and the printer was unplugged when I moved it from one computer to another. I probably should try cleaning it, though, as it has gotten a bit dirty with me having to take the drum unit in and out so many times.

I don't use the printer nearly as much as I used to, since most things can be e-mailed rather than printed these days. If I can't get it going again, I'll have to have a debate with myself over whether or not I really need a new printer!

My guess is that it's one of the little rubber pads that grabs the paper and feeds it in. They wear out over time. I had to fix one, one time. It's in that forum post I linked to.
But if you're not up for the diy fixit, as Snidely says, printers are pretty cheap these days.