Your lease is not valid until it is signed by both the landlord and the tenant. If the lease is for more than one year, there must be two witnesses to the signatures. Until the lease is properly executed, you do not have any rights to use the property nor do you have any action against the landlord for damages. You are stuck waiting for the landlord to sign the lease. if you are unsure of your rights or responsibilities, you should consult an experienced real estate lawyer in your area.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
Next time, it may be best for you to sign lease in person, have it countersigned and pick up keys at one time. At this point, as Counsel mentioned, you are stuck at the time frame of the landlord. In terms of enforcement of the lease without both parties signing, the fact that they have not endorsed your check is not helping your situation. Caution: if your landlord has not been organized and followed from the inception, you may want to think this relationship over.
DISCLAIMER: This answer is provided solely for informational purposes only. This answer does not constitute legal advice, create an attorney-client relationship, or constitute attorney advertising.