Internal fuse need replacing

Sounds like you have a weak battery, test the voltage. If battery is fine then your starter relay is the culprit. Clean all terminals in battery and relay, corrosion on the connectors will cause this too

You've not said the make or model of your camera, but with most cameras the power batteries also charge an internal battery within the camera, which does 'housekeeping' duties. If, as you say, it has been stored without batteries for a period, this internal battery will have run down, and needs to be replaced. Unfortunately, this is not a task that can be accomplished except by a repair centre, and this will be expensive.

It has spark and fuel when the fuse is blown too?

Remove the main battery and run the ac adapter only, if everything works fine the battery will need to be replaced, if the computer continues to shutdown the problem is most likely a bad cooling fan or it needs to be taken apart and given a good cleaning.

You are looking at having to replace the motherboard here, as the charging circuit appears to not be working. I assume the computer works as long as it's plugged in, so the DC-in jack must be OK

I would first double-check the "known good" power supply. If there is something bad wrong with the MB, it could have blown the fuse in the power supply. I have seen very few fuses on motherboards, they are normally in the power supply. If the power supply checks out OK, then double check the connectors between the power supply and the MB.

Well it's temping to put in biggfer fuses as the problem gets worse but the size of the fuses are to keep you from burning things up so you've from your probem with a 30 amp smoke test. The raditor fan wire is melted somewhere in the wire harnes to the wire for the trck lock or even key on circirts. the likly place to look is inside the stering collum. It takes the skills of removing the steering whel and the lcok plate and even then thats does'nt have to be where the problem is. You need to look under the dash after you remove the covers and use you nose to smeel for the burnt wiring and open up any thing the smells like it's been hot and anything the appers melted together. once a harness is found melted you need to seragete all the wires in the loom but don't cut the wires justy seaparte them. once you think you've got then all pulled apart so no bear wires touch each other or any meal parts put in the correct size fuses and see if you can connect the battery with out a spark. if you can you may then start checking to see what works and what does'nt.. This all sounds like too much work or too hard to do then you'll need to pay someone theat knows alot about car wiring problems to do it for you. I'll been doing this kind of work for the last 20 years and a'm alawys finding new things that are fried and burnt up. We all charge by the hour to do this work so the most experieced mechanic that works on cars like yours will probly find and fix the problem the fastest. therefore they may charge more per hour but their likly to get it right quicker and it'll stay fixed after they fix it.. This is the most likly kind of work to go sour after it's fixed cause they might miss a circuit that you use and they did'nt try. and as soon as it burns again it's back to the drawing board and if big fuses are use the fire can take the whole car.

Many cars have the cooling fan on a thermostat or time delay, to allow it to run for a short period of time after the engine turns off, to cool the engine off. You may have just never noticed it before. So I wouldn't worry about that.
Your real problem is the blowing fuses, apparently you have a short somewhere in your wiring. Putting in bigger and bigger fuses is a great way to set fire to your wiring harness. It's possible that the wire is pinched or chafed somewhere, and perhaps when you hit a bump just right, it touches and shorts.
You may have to take this to the Chevy dealer or a GOOD independent shop to have them chase it down. Unless someone out there knows exactly what this is, it could be a tough one to find.

I remember a recall on certain Dell laptop batteries due to their hot running.

Please confirm with your nearest laptop dealer ASAP as they have been known to catch fire!!!

bad battery.. RMA that back to where you bought it from. probably wasnt a new battery they sold you. id charge it from completely dead to completely full one more time and if you dont get at least an hour out of the batt then i would return it..