I haven't seen any standard free parking for elitie staus; I was recently charged $18 in Newport Beach at full-service Marriott, but was given free parking at full-service Marriott in Riverside, CA...supply and demand? Individual property policy? Have also seem some properties with "reserved parking spots" for elite members yet normally at properties with free parking the reserved spots are closer to the front and may or may not be a value add. So in my observation I don't think there is a blanket policy but wish there was as the parking fee to me (at certain properties) is another tax.
Better read it again. We may get free Internet service now but parking is one perk we will never see and the question had been posed on this site a few years back. The official answer from Marriott at that time was that Marriott (or the licensee) many times don't own the parking facilities and merely act as a liaison to the parking company. For that reason Marriott would not be able to offer Elite's free parking simply because for a lot of Marriott properties it would come directly out of their coffers. This response makes sense to me because I can't imagine pulling up to the valet at the Marquis in Times Square and having them "comp" me $45 a day for parking. However, Marriott does offer weekend packages at some hotels (such as World Center) which includes parking.
When I stay at a Marriott hotel I either pay or don't pay for parking according to the local rules. However whilst at one Marriott I often travel to a neighbouring one to take advantage of meal promotions etc. On these occasions parking is often charged, however I always get a refund from the front desk- no arguments.