My engine will not turn over?

I have an issue with my 2001 Chevy Venture, last winter our van would not start most of the time, it was garage kept, but would not start 90% of the time. We would need to charge the battery at least twice a week. We had a friend look at it and he found the "fuse wire" running form the battery to the fuse box inside (below the dashboard) on the passenger side, was corroded. Which he cleaned up and the van ran great until the winter. We had a new battery installed about 2 months ago, my brother in law found that the positive cable of the battery was not tightened properly (which he tightened), now we have another issue: We went to go start the van, and heard one click and that was it. Waited about an hour and the van started right away, the next day started like a champ, the next day turned the ignition the rear air compressor went on and heard one click, waited for the compressor to go off and it started. Today same thing. Turned the ignition, compressor on / off, after about 5 minutes it started. Any thoughts? I'll gladly replace the starter if it saves me the hassle of guessing from day to day if the van will start.

Hi thanks for the response, I'd have to hook at battery tester up to the battery to find out if it's at full charge. The battery is only a little over a month old, and when the doors open I hear the dinging and the security led is flashing on top of the dashboard. When the key is inserted and turned slightly all the dash lights go on, radio turns on, air compressor fills, AC or heat turn on. The first time this occured the Security message on the alert system did come on. We have not tried starting from the neutral position when this occurs. When you say in the cranked position the purple wire to the solenoid should be hot, do you mean the engine is running or the key is turned just before starting? I'm sorry I'm not much of a car guy.I have someone willing to install a new starter, but first I'd like to try to eliminate anything I can prior to making the purchase.

Thanks

Hi, I did bring the car to AutoZone today to have it checked out. They gave me two codes, P0442, and P0128, they also did a check on my starter and alternator and both came back ok. They said the voltage on the starter came back around 12v ( I believe that was the number) which was within the limits of still being good. One of the guys there mentioned it might be the solenoid that was sticking.

How would I go about getting you that information?

Ok, another issue that could or could not be related. The next day after going to Autozone to have my starter and alternator checked, the car started fine, but ran horribly. When pressing on the accelerator, the car sputtered (never stalled), took a long time to accelerate, the check engine light started flashing, then went solid as it has before due to the codes previously mentioned. The only thing that was moved (screw taken out and fuse box moved over) at AutoZone was the engine fuse box, since the battery poles are in a very difficult spot to get to. Once we got to where we were going I opened the hood and started to jiggle the wiring going into the fuse box and battery. After doing the the ride home was smooth. Could this be related to my starting issue? If so, how would I go about determining how to fix this. Assuming I have a short somewhere in the fuse box wiring.

Put a brand new battery in vehicle, can hear fuel pump kicking in, lots of power to controls, cluster lites all work, as soon as u turn ignition key too "start" there is nothing, no turning over, no " click" from starter.

When you turn switch to on position lights work. Radio works. Clicks when u turn key but wont start.U can bump from starter silenoid and it will start. Put differnt starter on but that didnt fix the problem. Put new ignition switch in but that didnt fix either. Any ideas would be appreciated. It wont start even in neautral. So its not the nutreal safety switch. Had ignition coil tested. Said it was fine.