I live in Ohio. I found a house for rent in Dayton, Ohio. I signed the lease already and I have a copy of it, but I haven't paid any rent or a deposit yet. I still want the house, but I've been dealing with my son, who is in the hospital in a town three hours away from me. My daughter was having some issues, so I had to tend to that as well before I could actually move into the new place.

My question is, do I have any recourse or is my lease worthless? I really want this house and I want to move in, but the landlord is giving me a hard time about my going to see about my children instead of moving in and paying him. I had to wait and see if my children needed anything and it turned out they did and I had to pay out of pocket for it. Can I enforce the lease or do I have no case?

WHEN did you sign this lease?
Did both parties sign it?
And now you are saying that the landlord wants out, but you want to keep it?
You can't just sign something and then dilly dally about forking over the dough. It doesn't matter who was sick and who had other problems. I would be reluctant to rent to someone who makes excuses for not paying the very first month; it doesn't bode well for the future.
Even if both parties signed the lease, the lease stipulates the rent and terms of payment, and you failed to get it off the ground. I just don't see a court ruling on your behalf.
A lot depends on the first two questions.

A lease is a contract. For a contract to be valid, the terms of the contract need to be adhered to.

So yes the lease is binding. But ALL the provisions of the lease are binding. So if you did not pay the deposit and rental by the due dates, you are in breach of the lease. Since you haven't taken possession, the landlord can claim you are in breach and rent to someone else and you will still owe what he has lost in rental by your breach.

Now if you promise to make him whole, he may continue to let you move in. So lets say you were supposed to move in Dec 1. But you now move in Feb 1, you still owe Dec and Jan rent. If you agree to pay that, he may let you move in. But if you don't he can cancel the lease, rent it to someone else starting Feb 1 and you still owe Dec and Jan. If he takes you to court you will lose.