Yes, this still all sounds like a bad connection somewhere to me, can't say for certain though. The "chunk" is typical for a bad connection. What happens is, when you power up the ignition, there is current being drawn from battery through various cables/wires. And there seems to be a good enough connection (at the mysterious bad spot) to allow current for ignition and display lights. When you hit start, it pulls more amps, which is more than the bad connection can handle, so the reaction is a short momentary engaging of the starter (which makes that cluck) and near immediate break in the wiring, which releases starter and kills lights. Now the current amps is lower, the display cylces, and appears normal again.
Check your wiring harness and connectors good. Especially check lower machine harness where cab wiring connects to it, just above hyd tank, then it runs along top of hyd tank and goes to fuse box and ECU. Check it good for abrasion points where it's rubbing against things. The ECU is located behind a panel on left side of machine. If you were sitting in the seat, and your left foot on pedal, it would be that panel next to your left leg.
You can pull the fuse panel out of the rubber boot with the boot mounted in front panel, it's a bit of a trick, but I've done it many times. If it's possible for you to jump start the machine, raise the loader arms and install the boom cylinder safety support. Makes it much easier to work on these with boom out of the way. Standing at the front of the machine facing the fuse box, take a flat screwdriver and start working the plastic fuse panel out of the rubber boot on your left side. The wiring comes in the right side, so you have to work your way from the left pulling it out. Once you get it pulled out on the left, it will pivot out of the rubber boot. Keep in mind, the wires don't have any excess, it will only allow you to pull it out enough to get a look at the backside. If you have to do any repairs in there, you have to pull the rubber boot out of the mounting to pull it back from fuse panel. The two bolts located just below the mounting of the rubber boot removes a retainer plater for the bottom of the boot, remove that retainer plate and you can work the boot out.
The fuel solenoid, kinda working on memory here, maybe Mrfixit Paul can remember, but I think it's controlled by both the fuel relay in fuse panel and ECU. The three wires, black-ground (controlled by ECU), red-12V (controlled by fuel relay), and white-12V (I think controlled by ECU). The white wire can only have power on it for about 5 seconds max or it will toast solenoid, so it has to be controlled by some type of time delay which make me think it's controlled by ECU.
Can't be much to these things? Well, not really. But pretty much everyone here that knows me knows what I think about them, working on a Bobcat is like sitting on top of a porcupine while down in a hole. Uncomfortable little critters to work on.