Have you thought about taking your machine to Auto Zone to let them scan
your computer for stored trouble codes?

Do you mean by "giving it gas" that you are pumping the accelerator pedal?
If your fuel pump is bad or if the injectors have problems I don't see
offhand how "giving it gas" can circumvent those problems.  Maybe I'm
missing something.

Finding a stored trouble code, if one exists, should quickly lead you to the
culprit.