Car won't start at

Hey guys, this is my first time posting on a forum,
so I hope this goes well. I drive a 2000 Mustang GT.
Recently, my car won't start, Only sometimes it'll
start up. I know it's not the ignition switch, because
sometimes if I get my car started (push start) I'll turn
it off real fast and than I'll turn it on again and it fires
right up, but if I turn it off and wait like 10 seconds it
doesn't start. When the car doesn't start, it doesn't
crank at all, I don't even hear a click or cranking
sound. My lights on my dash work just fine when I
turn the key. I thought it was my clutch safety
switch, so I by passed it and it still didn't start. I'm
not sure if this has anything todo with my car not
starting, but acouple days ago my led wire started
getting really hot and starting smoking so I
disconnected the leds. The led were fused to my
fuse box fwi. I checked all my fuses and all checked
out to be fine. Anybody know anything that might
help??