Re: Car starts but dies -CPS WAS REPLACED 6 MONTHS AGO-
Was your replacement CPS a Bosch one? I've heard of off-brand replacements from parts stores dying in a matter of days to weeks, so I wouldn't rule it out even though it's only been six months. I'd pull codes first as it's the easiest thing to do and could point you to something immediately.
Otherwise I think your troubleshooting is pretty sound. Trying a jump and a camshaft sensor replacement both sound like reasonable ideas, although I think the camshaft sensor will generally set a code.