As stated above, park the car in a quiet location and listen at ground level (lean over as far as you can with the door open), you should be able to hear the solenoid clicking when pressing the shifter button (ignition on). Don't confuse this for the clicking from inside the dash where the OD relay is located. If you hear the clicking under the car, odds are the relay and solenoid are good. Make sure fuse #11 is in good order.
Otherwise the most common failure is with the relay. On your model, even if the dash light comes on when you press the button, the relay could well still be faulty. Best to pull it, pop the cover off and inspect the circuit board for any cold-cracked-failed-fried solder joints, re-flow as need or all of them. Access the relay by removing the glove box, relay is located below the center dash vents. If the relay is in good order, check under the car, use a test lamp to make sure there is both sufficient voltage and current reaching the solenoid connector; and if so, odds are you need a new solenoid. I'd pull it off and bench test it.
If replacing the solenoid: The same OD solenoid is used on most all automatic equipped '82+ 240/700/940 4 cylinder cars, so you might be able to find a good used one, but otherwise about 60$ for a new aftermarket. Jack up the entire driver's side of the car, clean the area around the solenoid first with brake cleaner to minimize dirt contamination, be ready for some fluid leaking out, but it shouldn't be too much. Two 12mm bolts, flex head ratcheting gear wrench works best.
For additional reference:
http://www.threefattigers.com/Protocore/Volvo/ODsolenoid.htm
Note the insulation on the white wire that exits the shifter is a common failure point where the insulation fails and the wire shorts, damaging the relay.
It's nice to have it on all the time as it helps when in low gears for round-town driving mileage
On an automatic? Still not going to shift into OD until about 35 mph.
I hear 240 OD solenoids are really super twitchy. The perfect fix would be an M47 5-Speed, though.
93 240 manual was an M47. 240 automatic OD solenoid is the same as found on almost all 4 cylinder RWD automatics, not a part I would describe a twitchy though.