Yes. You don't have a fuel problem. The symptom of stalling when you take
your foot off the pedal is because the computer is not adjusting the IAC
(idle air control) motor properly, thus not allowing enough air into the
throttle body when the throttle blades are closed (foot off of pedal). That
could be due to a number of reasons, one of them being a weak battery.
Put in a fresh battery, start the vehicle, and then measure the voltage
across the battery terminals. You should read around 13.8V - 14.0V, in
which case the alternator's doing it's job (if you only read about
12.5V-12.6V, then your alternator's shot). Do NOT use the old method of
disconnecting the battery while the engine's running to test the
alternator... that works fine for non-computer-controlled engines, but the
electronics really don't like dealing with the voltage spikes that the
alternator produces (which the battery absorbs and smooths out - think of it
like an electrical shock absorber).
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