Big Problems.. Need help!

[BlackLX]

Last night i started the car it started fine.. but this morning when i started it .I found out that the car has lost power when im stomp on it ... and the light would seem more darker.. so i tought myself maybe a battery problem.. i went to some shop when i was in the parking lot the car suddenly seem to buck like it was going to die.. it suddenly die but the lights ,warning lighs were still on so i push the car to a parking space ,went inside the shop bought a new battery i replace it and when i put the key in ignition i didnt heard the huum sound of the fuel pump ... the starter wouldnt even crank ... so i call a towing to get home..i tried to figure out whats the problem... i check the battery ... the alt... when i put the key in ignition i got all the warning lights..the lights are working all even the heater.. but the starter wont seem to crank and i cant hear the fuel pump umm sound..so help me out the car sitting in my garage i need to solve this problem..one thing i did notice it was that the starter would still crank when i put power on it with a 12v source..help me out ! i need help

1992 Mustang 5.0 (91000 miles)