Where to start I guess the car dies when you shift it into gear

I got a whole list of problems I'm not very
mechanically inclined I can handle the basic
stuff that's about it. but there's a whole bunch
of stuff that started going wrong at one time
and I think it's all connected but every
website tells me I need to list it one question
at a time the problem is I don't know where to
start so I'll just name the main problem I'm
having now the car will run in ideland either
park or neutral but as soon as you shifted
into gear it dies instantly no spitting no
sputtering it just dies. to give you a hint of the
other stuff that had been doing that led up to
it everything happening all at once it ran hot it
was blowing air out the tailpipe really fast
and accelerated on its own and then
eventually it killed the battery I had so I
bought a brand new one anyways one
question at a time they say so my question is
what will make it die when I put it into gear
from either park or neutral?PS I'm calling this
a GT because I've researched both and I can't
really tell the difference and either one
because in 2005 they were made with the
same engine and everything so I'm not really
sure how to tell the difference but I think it's a
GT