Car turns but won't start.

Bought this car about a week ago. Everything was
fine until I let it sit through the weekend in Chicago
(was pretty cold this weekend too) . She started ,
ran n drove fine before she sat over the weekend. I
went to start the car today and it turns over but just
won't start. You can tell she wants to start but just
can't. Engine turns over just fine. It's not too fast or
anything like that. No grinding noise or anything.
Just literally will not pick up the last step it needs
to start. However when I turn my key into the "ON"
position I do not hear the fuel pump engage like I
have in my previous vehicles. Jump starting the
vehicle does not work either. Still turns just won't
turn on. All lights turn on . Headlights (but very
dim) interior lights and the radio all work but they
do dim out a bit when trying to start the car. Worst
of all I cant drive it anywhere to get it diagnosed.
So I need some helpful tips from you guys
hopefully. Only 20yrs but I do love working with my
hands so give me some ideas to test the waters
with please!