Car won"t start even after jump!

It sounds like it might be vapor locking.

have a load test done on the battery as I suspect you have a dead cell or broken cell bridge.

Open up your key and dry it first of all.
Then retry.

Or you could try using your spare set of keys.

Knowing the poor quality of this remote I would buy another remote on eBay and that will likely solve the problem. Here is a link to an eBay auction. Just $17.99 and free shipping.

sounds like a problem with the ignition barrel.the wiring is loose or the connectors are loose or the barrel is faulty,unless thse are all run from the onboard computer.

By manually unlocking the driver side door with the vehicle's key, this should disarm the alarm system. If it fails on the first attempt try turning the key to the unlock position twice in a row. This is the standard security procedure in case of remote loss or malfunction.

try resetting the computer
disconnect the positive cable to your battery, leave off for a minute then reconnect

I would try first replacing the battery in the remote

sounds like fob circuitry is getting a bad connection... or it's dying... pull fob apart and gently clean the button electrical contacts

By no power, do you mean the lights and other accessories don't even work? If so, I'm not sure that's a security system -- they usually only kill the starter, but I'm not sure about that one specifically. Try arming and disarming the system and see if it works then. If no interior lights are working, etc. you probably have a very dead battery or possibly a bad connection. Hook up the jumper cables again but leave them on with the working car running for 10 min or so, then try to start it. Batteries can get so dead that they won't jump right away, especially with light-duty cables.