My father meets the Medicare qualificaions to be reimbursed for most
of the cost of an electric wheelchair.  In other words, if he buys a
new electric wheelchair, and submits the proper paperwork, we know
Medicare will participate.  My question is, Will Medicare participate
if he buys a the same model wheelchair,used, from a private party?

No. Medicare does not purchase used equipment.

Medicare will rent some equipment, especially if someone may need it
for a short time -- and this is a good way to try out different models
and features of power wheelchairs.

There is a robust secondary market, where you can buy used power
wheelchairs and scooters. Visit
http://www.wheelchairjunkie.com
for much more information