I think you will get better and more helpful answers if you are more specific. I might have some but ideas please add some more information:
What kind of routine do you follow?
What kind of activities does he do during the day? How much is unstructured, structured, and active play?
Does he participate in any groups or go to child care?
Is he in school (preschool or kindergarten)?
How much sleep does he get uninterrupted? (At night or in naps.)
What kind of limitations do you put on his behavior? Is he aggressive or just energetic? If he is agressive is it because of specific triggers or is it when he is tired in general or all the time?
I think a little more information will help anyone offer more specific advice--I will check back later to see if you have anything to help clarify and then maybe I'll have some advice. :)
UPDATE:
Thanks for the added information! :)
He does not sound in need of medication AT ALL. Children his age require a great deal of active play every day. My children are literally climbing our bookshelves and dancing on the dining table on rainy days because they can't be outside running amok. If he is in regular school and there even a half day, he still needs a physical break. Children who watch too much television have much shorter attention spans for school and are not getting enough activity. It can be hard with a relative providing care, especially if the relative is not able to accomodate the active play, but it is important.
My children, sadly, watch too much television as well, but we try to keep it to a total of less than a full length movie. I use that time to clean, cook, make phone calls, or to help them relax right before bed (sit still and unwind) or while giving my youngest his nebulizer treatments. The recommendations is 2 hours or less for screen time and it can be hard to remember to include computer time in that total. There are definitely days we go over that (mommy home sick) and days we do not turn it on, so it balances out.
I don't know what PSP is, but basically he should be getting a lot more active play time. He is old enough for organized activity at rec centers if your area offers them in the summer. If you are struggling with his grandma meeting his activity levels, try to arrange for easy active places she can take him--a fenced in park, a children's museum, getting a family zoo pass, or again lessons or sports activities with an instructor. If my kids are awake, I try to work out with them (when I have the energy), so we are all doing something active together and burning some of that evening energy off (their energy, my desperation).
I hope some ideas help. There are children who have issues that cannot be controlled by any amount of activity--I have an adult friend who has struggled his whole life with attention and focus and runs over five miles every day. He finally got himself diagnosed and on medication and feels he can function normally. That is not typical. Try some of the suggestions you're getting here and give them time to work. It will be hard weaning him off of television, but set some limits for it. You could even get a special stop watch and get him on board with clocking his screen time--get him excited about his active time (he probably won't need much encouragement). :)