You let these people manipulate you. They dictated the terms to you. THIS IS WRONG! You need to have a strict set of rules for move in and lease signing. All this business of paying one amount, then another, and then they did not do what they said. Do not let this happen again.
If they want to move in in less than two weeks issue a Rental Binder (LPA form) that lists a NON-REFUNDABLE HOLDING FEE of one months rent. Then list a lease signing and move in date within two weeks of taking their fee. Get a cashier's check or money order only. All the rest of the move in funds, (first, last, and SD) is due on the lease signing date in certified funds and the power (and renter's insurance) has to be in their name. If they don't come through they lose their holding fee. No full move in funds, no keys. Strict policy and don't waver.