I have put in a gently used coil top range in before a couple of time (because they last forever and fairly easy to move and install) but with a refrigerator or washer or dryer or dishwasher, I just get a new one. 

Not the vents but the inside coils.

I am replacing coil tops with glass tops in my unit and they are C minus to D but my rents are also increasing by 50-75 per month after renovation.

I've got coils on the house now to help reduce the chance of them freezing and a bucket of salt at the front door (the salt destroys the deck).

This time I opted to replace the coil only.

Have they vacuumed the coils lately?

I capitalized on the architecture of the building and rather than gutting the place, refreshed the original cabinets, installed period-appropriate lighting fixtures, got a new stainless fridge but found a vintage Frigidaire wide-coil stainless steel cooktop and installed a new stainless 18" dishwasher (where there previously was no dishwasher at all).  

Burned out oven coil, etc.

If you have a/c with the furnace, make sure there is a secondary drain pan installed under the evaporator coil to prevent water damage when the primary drain gets clogged.

Like most other things on houses 85% of the work is FIELD WORK which requires no brains, just a hammer (air nailer!).