First off, for $80 you got a deal!
That motor is by far the most commonly used unit for these compressors no matter what brand the compressor is, ditto for the pump. The usual failure for the motor is one or both of the capacitors on the motor and I bet if you pull the covers off the side of the motor one or both will be swelled and/or ruptured so check that first, even if the motor is toast you still got a heck of a deal. If the pump ran for a year and never had the oil changed at all then the color and the metal shavings would not be unusual but if the crank and rods are still sound you will probably be OK here, for a while anyway. With the belt off turn the pump flywheel back and forth and see if there is any slack that would indicate a rod loose on the crank and also listen for any "clanking" sounds. Most likely the pump is OK and the compressor was down from motor failure so if that is the case you would be money ahead to just scrap that Emerson and find yourself a good 15 AMP motor, maybe even another Emerson if you can get a good deal on one but a Baldor or GE would last a lifetime! There was discussion just in the last couple of days concerning a burned out compressor motor (another Emerson) and you may want to check for the same problems as a cause for this motor failure. IMMEDIATELY upon starting your new or repaired motor watch the compressor closely as it builds pressure for the first time and make sure you do not hear any hissing or other unusual sounds coming from the pressure switch. When it reaches shut-off pressure you should hear a short burst of air from the cutoff switch that would indicate the unloader valve is working, failure of this unloader system is probably the biggest cause of motor failure on these compressors. When the tank pressure falls to the startup level and the motor again kicks on make sure it does so easily and does not start slowly or try to stall. If the motor, with pressure in the tank, does seem to be under an excess load at startup then make sure the the plastic (probably plastic anyway) line from the pump discharge to the pressure switch (that's it going to the bottom of the pressure switch in the pic) is intact and not plugged. Also since this thing has been disassembled you want to make SURE the check valve that prevents pressure from flowing from the tank back into the pump is still in place, air should b able to flow from the pump into the tank but it should not be able to reverse direction and flow back into the pump. Hope this gets you started in the right direction and that the motor is the only problem but even if you have to replace both the motor and pump (not likely) you still got a really good deal since just a one year old tank by itself is worth a lot more than you paid.
BTW, when looking for a motor just remember that the Emerson was probably over-rated and and a 15 AMP motor is what you will be looking for. That 15 AMP Emerson was around 3 1/2 HP regardless of what the compressor labels claim which may have been as much as 7 "peak" HP!