Engine running, AC switched on, temp settings on coldest.

Try removing the wires to the pressostat, located on the AC line close to the firewall. Use a wire or paperclip and jumper the 2 leads on the wire. That should make the compressor engage.

It could also be the clutch gap is too large on the compressor. Tap the center of the clutch with a long stick being mindful of the turning belt. If the clutch engages, the gap needs to be corrected.

You could have a faulty AC relay.
EDIT: or a bad fuse:

http://www.brickboard.com/AWD/volvo/1478543/S70/.html

That is a start.

There is a long thread you can search for that has a similar problem.

Klaus

--
Always willing to listen, just not able to take direction.