mx5cartalk.com

does the buzz noise happen when the engine is off but the key is turned to the on position?

I remember reading that after a period of the window straining because of dirty guides and lack of lubrication, the cable that moved the windows can break.

I think you can buy replacements off MX5Mania.


edit:

here's the listing:
http://www.mx5mania.com.au/product1225.htm

pop the door trim off and have a look to see if the motors are actually working, it's very simple. you should be able to see if the cables are intact and spinning etc...

It could be switch contacts. They're notorious for getting a carbon build up.

You'd need to get the switch out of the console (not a hard job), disassemble the switch and clean the copper contacts with fine sandpaper or similar.

More info here.