Parking at all or the parks is $10.00 a day. Sorry, there is no multiday discount. If you pay at one park and hop to another with your car, save the receipt from the first park and show it at the toll booth and you will be allowed to park there for no additional cost.
While there is a way to get away with parking at DTD and then using Disney Transport to get to the parks, I don't recommend it for many reasons. First is the time involved. You either need to bus to a resort and to a park or boat to POR and bus to a park or walk to SSR and bus to a park. Now in all of these, you waste tremendous amounts of time and also run a greater risk of car damage. DTD is a parking lot in a lot of turmoil. The average time of a car in a space is about 3 hours, at a theme park it's 8 hours. You have higher amounts of vehiculae and pedestrian traffic in and around your vehicle.
IMHO, just pay the $10, it's faster, easier and most likely, in the long run, cheaper.