C280 rear brake question (vivrating)

My 98 C280 ( which I'm trying to sell) recently had a problem where the brakes seemed to throb or vibrate at the wheel rotation speed when brakes were applied .Not wanting to sell it with any problems. I changed the front pads and rotors that were quite worn to no avail. When I opened the rear brakes I found that the inner shoes were not moving. All the wear was on the outers pads. Upon removing the calipers I found that the inner shoes were apparently rusted in Place. .When I removed the shoes the caliper would respond to the brake pedal and move teh piston out the boots are in condition.
I've odreded both new disk ( the insides were rusty) and pads and wondered what if anything other that cleaning the rust from the calipers I should do to make sure I get it right.
The car was not driven for several months and I'm wondering if that contributed to this failure
Thanks in Advance
Boborann