You have a loose connection on one of the battery cables... (or corroded)
Start at the battery and make sure both cables are clean and tight. Then follow both cables to the other end and make sure that connection is clean and tight.
Check all 4 connections, then start.
If this doesn't work, get back with us.
Dave
Edit:
Check both cables themselves while you are at it!
If the cables are old and corroded, you should just replace them. It will be obvious, they will have a powdery substance coming out the ends of the cable itself. The copper inside can be brittle along with the corrosion. Another thing to look for is the cable being swollen and very flimsy. This can happen if the cables are corroded along with exposure to oil, grease, or gas. The insulation almost feels like it is melting (without heat). If any end of the cable is a bolt on type, where the wire is put into the connector then bolts are tightened to hold it in place... The connections could be corroded or loose without the wires and/or connectors being bad. Think of these as just another connection that must be cleaned, tightened, and checked occaisionally just like the battery post connections themselves.