It appears from the description of facts that the landlord was obligated to clean the apartment, did not do so before the move-in, then presumably the tenant got the cleaning done and submitted the bill to the landlord, who accepted the bill. That part of the contract has therefore been completed, though not in the originally planned manner: the landlord has not breached the contract (since the alternative of tenant arranging the cleaning was accepted).
Depending on which state this is in, a tenant can terminate a lease for certain reasons: most usually if the place is uninhabitable, and possibly if there is a substantial breach of the lease. There will be procedural requirements about giving written notice and so on. A tenant can not unilaterally terminate a contract because the tenant is fed up or because a landlord lied or provided the required service in a different manner. (A tenant could repudiate a contract, and face legal consequences). It appears that the tenant repudiated the lease.
That repudiation seems to have taken two forms. One is, presumably, telling the landlord "This lease is over, I'm leaving", and the other is by not performing part of the contract (paying first and security initially, and then by paying only half of the initial obligation).
What comes next depends again on the state and on the duration of the lease. If this is a yearly lease, the tenant would owe $21,450 for the duration of the lease. If this is a monthly lease, then it depends on the advance-notice conditions and whether notice was properly given. Let's say the lease requires 20 days advance notice and such notice was given more than 20 days before the end of the lease. Then the tenant owes the first month's rent (and also the security deposit, which would be refunded minus any damages): the first month has been paid. If notice wasn't given until after two weeks (less than 20 days), then the lease would terminate (lawfully) at the end of the second month, so the tenant would owe $3300.
If the tenant moved out before the end of the month and the landlord was able to re-rent the unit within that period (let's say notice was too late but he filled the apartment as of the start of the next month), then he might not be able to hold the tenant to the second month's rent (depends on state law and lease). However, if the unit were not rented, then the tenant would owe that second month's rent. In no situation can a tenant just leave a lease and demand a portion of their rent payment for the unoccupied time.
The tenant can get a lawyer, in case there is any hope of mitigated the legal damage that the tenant has apparently done to himself. In the most optimistic circumstance, a monthly tenant who gave sufficient notice could be free of their financial obligation with the $1650 that they paid for that month, and if there was no damage, that would be the end of that. The tenant would still be in breach of his obligation, in not having paid the security deposit, but landlord might not want to pursue the matter if he knows there was no damage.