First things first, never use dish detergent
it removes all wax and sealers. Bad.
You should go out to the auto store and get a jar of 3m detailers clay.
Get some good car wash and rub out the entire car including the windows.
It works wonders removes all dirt and debree in paint. It wont harm the paint. Its actually good for it. Then get youself some good polish and wax on wax off.
Never use wax. Wax seals the paint and paint needs to breath. Symptoms of a heavy waxed car over time is cracking and crows feet from lack of breathing.
Hope my two cents helps.
RAY
