I honestly cannot fathom why you would want to stash, and then invest energy in providing an environment for, all that computer equipment. Sell it off and when you need it again, get new stuff that is up to date. But it's your stuff and your money, so let's keep going:
I don't recommend the portables. I just don't. They're terrible. Seriously: ANY window unit will be a better solution. ANY.
The charge controllers would be useful but to run any AC you'll either need to get a DC unit (they're out there but pricey) or else an inverter, along with sufficient battery storage to keep the system going. This will necessitate some extra space, so you might be better off moving up to a slightly larger shed to accommodate the power hardware.
The Amazon link you provided for a lighting charger, that is a small device intended only to keep a few light bulbs light for up to half a day. It won't power an air conditioner at all, it cannot deliver the necessary voltage or current.
To provide plenty of power for operating your AC and storage for getting through the night and a day or two of cloudy weather, you need a system more like this: