Have had it at the dealership

Question:
Have a 1995 Jeep Grand Cherokee automatic with 226,000 km on it. Have had the starter replaced but still have problems starting jeep. Will start okay a few times but then will need to try up to 5 times (turning the key - no noise but lights on dashboard come on, etc.) before it will start. Any suggestions on what the problem could be?

Already Tried:
Have had it at the dealership - they replaced starter but that did not help at all. The start problems usually happens when the car has been parked for less than an hour but this week it started even when parked overnight. It will be okay for about 4 time parked but then will not start. Have to turn the key in the ignition a few times before it catches. The dealership has no idea what the problem is as the car works okay when it has been left there (left twice, overnight for them to test during the day, etc.) Any ideas would be appreciated.

Answer:
I would definitely suspect you have a problem either with the cables for the starter. Or you have a bad or failing starter relay. But lets get the OBD or on board diagnostics. They can often point in a good direction.

Here is general procedure for getting engine codes by using the flash method.
Turn the key from off to on three times within five seconds. Then watch the CHECK ENGINE lamp. (odometer on digital odometers will show codes not flash) When you hit the proper rhythm ( this varies some from vehicle to vehicle and takes a few tries sometimes ), the MIL will stay lit longer than normal, go out and then start flashing.
Count the flashes. There will be short pauses between sets of flashes to indicate you're going to another number. The last set of flashes will always be 5-5, or code 55, which means end of test. All the codes will have two digits to them. You can repeat this as many times as needed to get a feel for how it works. If the PCM or battery has been disconnected within the last month or so, the first code you'll see is 1-2 (code 12) which indicates a recent loss of memory. be careful not to misread numbers so like 1-2 becomes a 3 or 2-3 becomes 3-2. Do this a few times to check and always write them down for future reference. Remember these codes do not say parts are bad only that they got or receive a bad signal. SO it maybe part before or after them that needs to be replaced.