Engine will not turnover

Six cylinder all wheel drive automatic 90,000 miles.

My husband and I have been driving this van for over two years with no issues and recently just drove it over 1,000 miles with no problem. I went to leave my office at the end of the day a week later and the van would not turn over. Lights, radio, etc, all good. Called for service and jumping the van failed. Took it to the garage, repair guys charged me $80.00 for diagnostics and investigation. They believed to be a loose wire to the computer. Could not find it and the fees were adding up. :-( We suspected the starter but the garage would not replace it. We waited until the van would start again, paid the fees, drove it home and parked it in our driveway. Within the last two weeks we were able to start it (did not drive it) three times out of maybe fifteen attempts. Twice in a row one day and later that morning it did not start. Tried another day around lunchtime thinking maybe cooler temperature outside and the van started in about eighty five to ninety degree weather. At this point we do not know what to do. Can someone offer some suggestions? We did not hear anything else besides the computer or loose wire. My parents had a similar issue with their 1996 Dodge Caravan and actually had to rock the van to start it, does not work for me. :-) They replaced their starter and fixed their issue so they figured there was a short in their starter or some failure. Any advice would be greatly appreciated.
Thank you,
Smurfette