My everlast jumpstarter will not charge

If it's new take it back if not go on their website and download a manual

Those have a 1 year warranty so depending on its age it is probably due for replacement.
They should be charge once a month or after each use.

all the jump starts i have seen have a deep cycle battery that is sealed - i would not run something like an air compressor motor with low voltage - it can be discharged almost flat , but do not leave it long before charging back up - low voltage =high amps on motors

Get a recharge cord for the unit, plug it in and recharge.

The charger to a Jumpstart charges at a low rate (300mA to 500mA) and will not push enough current to start a car. Best to have Jumpstarts recharged every 6 months to be ready for emergency.

Most of them came with a AC and Dc cord to charge them

Hi, usually after you drain the unit down it will take up to 4 hours for it to charge up 100%. but do not leave it on the charger all the time when not in use because this decreases battery life.

You should be able to try it immediately, or whenever you need to.

The TV needs a fairly stable and well filtered 12V power supply. A jumpstart box is 12V, but is I seriously doubt that it is anywhere near filtered and stable, so most likely you would smoke the TV.

Hooking the TV directly to a 12V battery is just fine, as long as the battery has enough current to run the TV.