If you've already got an ethernet cable to its location you could try using "poor man's power-over-ethernet mode B", which doesn't require anything but a little wire hacking.
10-T and 100-T ethernet uses only the second (orange/white) and third (green/white) pair. The first (blue/white, pins 3&4) and fourth (brown/white, pins 7& pair are just floating.
If the power drain is low enough you could tie the blue/white lines together for the (+) side of the 12V power and the brown/white lines together for the (-). Fuse it at no more than an amp and a quarter at the sending end (to keep the wire from setting your house on fire) and tie it to the power input on the modem end. If the modem's internal regulator is good enough and the current low enough it will just work.
People have powered WRT54Gs at 12V 1A over a hundred feet of cable this way. The wire drops the voltage to 11 or so but the modem/router then regulates it down to +5 and is happy.
Cat 5E uses #24 AWG connectors, which the TIA (telecom industry assoc.) rates at 360 ma/conductor at 50V - if you want to put 100 of 'em in a bundle at 45 degrees C ambient. So if your modem has low enough draw I'd fuse it at 3/4A just to be safe - within about 4% of the TIA recommendation. And I'd make REALLY SURE the two conductors of each of the pair you use for power get tied together so all the current doesn't end up on one of 'em.
(REAL power-over-ethernet starts out at 48V, can "phantom" on the signal wires as well as using the spares, and goes through a bunch of handshaking to make sure it has a standards-conforming device at the powered end and doesn't fry something that wasn't ready to be handed 50 watts on a comm line.)
Wikipedia article here.