Sounds like the engine speed sensor has failed. (AKA rpm sensor). This is mounted in a somewhat difficult location right behind the head, on the top of the trans bell housing. It senses holes in the edge of the flywheel, and times the engine based on the count of holes. They are prone to failure, and yours is probably due for a replacement. You can do it yourself, but be certain to use PB Blaster or Liquid wrench when gettign it out- if the bracket breaks, the trans has to be dropped to get at the little bugger.
The cable from it has a paint band marking it - either yellow paint or white paint. I believe yellow is original Volvo, white is the replacemetn part.

Without this, the ignition computer never fires the coil, and the fuel system won't turn on the pumps.

It would be a good idea as well to replace the fuel pump relay at this time as well- that's under the dash, on the firewall in front of the glovebox. White relay 1 inch by 2 inch. It has a date on it, and if it's original, it will leave you stuck sometime soon. The old one in my 91 died in February.

Good luck!
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Rob Bareiss, New London CT ::: '87 244DL/M47- 221K, 88 744GLE- 202K, 91 244 181K, 88 244GL 145K