Car will not start as power is being drained

Check current drain with car off. Start removing fuses until one makes the drain go to zero. then diagnose that circuit. It could be something silly like a glove box light.

I had a similar problem years ago. As long as your dash lights come on, it's likely you can use an external pushbutton switch to run the starter. There are likely just 4 wires on the ignition switch. Power from the battery, and switched to:
accessories
main car stuff (dash lights, ignition, signals, etc)
starter.
splice in wires from battery and starter to new switch, and you're good to go. This worked for years on my old car.

can i buy a comma? says vanna white?? LOL !
ok, the battery drains, so you got a DRAIN, called phantom drain.
or dark current.!!
we use a thing called an AMMETER (DMM) to find all drains, easy

do you have one, want to learn or just wanting wild guessing.

on any 08 liberty, we check the scan tool data.
oops it shows battery low, wow even the PCM sees that.

new batteries do not fix drain.
nor dead alternators.

get it serviced, by a pro. ?

1: charge battery (rested its 12.6vdc )
2: start engine, scan tool shows, what DTC errors (post em')
3: battery voltage is , 13.3, to 15vdc running, if not charge system is faulting.
4: ok all that is ok, i then key off and measure bettery cable neg lug drain current, if 0.010a to 0.040a its ok, if over 0.1 amps its a drain.
we then find the drain cause, ASK? its not hard with a meter.
but i bet all you wanted is a wild guess.

If dash lights are popping on and off, and the cruise turns off, then you are experiencing an interruption in power (as if the ignition is turned off and on). You or the mechanic did not specify which fuse blew. That could just be coincidence. Considering you have the battery light, there is a chance you have a charging system problem. The car uses power generated by the alternator when it's running, and switches to battery power if the alternator stops outputting. If the car is using the battery, it will drain and cause power interruptions and ultimately, kills the battery. Check the serpentine belt, clean and inspect battery cables and posts - tighten clamps, get the alternator and battery tested (Autozone will do this for free). I'm thinking bad alternator. The only other thing I can think of is you have a short somewhere in the ignition wiring, or a faulty ignition switch. But the fact that it got progressively worse speaks to the charging issue. If you want to test the charging system yourself, let me know and I'll post a basic procedure.

When you turn the key to on, not start, the warning lights and gauges on the dash should all be on. If not, it may be a problem with the ignition switch. Check the maxi fuses under the hood if the switch is not getting power to it. If it is getting power, it could be a bad switch-the electrical portion, not the key cylinder.
If the security light is on, it may be an immobilizer fault-the security has immobilized the start circuit.

first thing to do is get the car not to crank and check for power to the starter. if the starter has battery power and signal from the ignition switch then the problem is the starter. second thing is to check the plug at the trans range switch. the connector may be loose since you just had the trans repaired. ground may be an issue but not likely since the dash lights and other things work. GOOD LUCK.

The on reason that comes to mind is that the key reader in the ignition switch is defective, they do act yup m,ore in hot temps.u

Same Thing happened to mine i had to hook up a push button to start it

One possibly/likely problem is that the ignition circuit is cutting out. I had this same issue on a car (malibu) and found it was an intermittent ignition switch connection. Replacing the ignition switch fixed it for good.
One thing that will really help you is to notice you dash lights when this happens. If the dash lights go out when the car stops, then this is it. If the dash lights (ignition) stay on, then you have another issue.

yes the switch would cause that problem with the brake light but not the dash lights, these cars had problems with the ignition swith and the chip reader on the ignition, hope this helps.