Car randomly not starting until jumped

Check your wire harness and battery cables, they may not be making a good electrical connection. A frayed end could be causing a loss of voltage. You will need a ohm meter to check for continuity along each cable. (You can get a decent meter at Walmart or any parts store for around $30.) Of course your problem may be more serious than an intermittent electrical connection, especially if your car was ever in a flood, you may have one or more bad computer modules, or a bad ignition module, that would require a dealer scan tool to look for, something a local mechanic shop might lack.

Just the fact that as soon as you jump it, it starts right up, is why I suggested a bad battery cable (when everything else is new; battery, alternator, starter)