You mean, you cleaned the battery connections? The no-start sounds unrelated (possibly). You might also:
1) wiggle all of the fuses to ensure they are properly seated and no oxidation under the contacts. Inspect/wiggle the PCM harnness connections
2) Quadruple check grounds again, and loosen/re-tighten the starter wire
3) Keep an eye on your starter solenoid. It's possible it is starting to fail. (it could act how you describe). If its an original starter, over time, the copper contacts inside the solenoid corrode away. Each time the starter is engaged, there is sparking the precise moment the two contacts meet. Over time the arcing wears the contacts down to the point where it can't quite get a good connection. During the initial stages it can create an 'intermittent' crank/no-crank situation.
4) Starter switch? The starter is engaged after the switch tells the PCM to engage the starter.
5) Have your battery load-tested. About 3 weeks ago I ran a number of errands in town. Went to a half dozen stores in my pick-up (not H3) to get supplies. Got to the jobsite, all was well till the end of the day, no-start! A lot of wierd dash light blinking and bad fuse warnings on the cluster message center. Yeah it was really frustrating, like you say, b/c for me I worked late that day ...till dark, and everyone had left. I wiggled all the wires, connections, ohmed out the fuses (I happened to have a multimeter in the truck), no difference. Fortunately it was fairly close to home, had wife pick me up. The internet is full of "Failed PCM" stories and fixes. Next day charged the battery up for hours, still nothing. Put a battery load tester on it later on -- voltage was right on, load test was a MAJOR FAIL. Needle dropped like a rock. Battery was old, but not that old. This truck isn't off-roaded and rides like a car. Battery must have broken apart internally. New battery and she's 100% now. Maybe pick up a Harbor Freight batt load tester or see if Autozone can test yours. Just to be sure. Esp with electric brakes, perhaps putting yer foot on the brakes (as you go to re-start), possibly it could draw enough current that a weak battery could 'flake out' a pcm signal. (just speculation)
6) Check you spark plugs for worn edges, or perhaps a platinum electrode (node) may have fallen off.
7) Vacuum and/or PCV. I had a vehicle with a hole in a cracked plastic PCV pipe that would cause erratic idle.
8) Possibly you might ohm out the coil packs. That wouldn't cause a no-start, but could lead to a rough idle.
9) Consider PCM (after you've exhausted everything else) -- Generally speaking everyone thinks 'black-box' is the problem right away, but it rarely is. It's the last thing on the list I would personally pursue, personally, but if you suspect water may have gotten into or around it, or see evidence of corrosion, then it's something to bump up higher on the list.
**If you go to any of the OEM manuals they pretty much start the troubleshooting trees this way; Work from the most common issues to the least common problems.
