94 Jeep Grand Cherokee will not start

https://www.youtube.com/watch?v=AvLbb48tQPw&t=422s

Wow. No, you need both cables on the battery for the vehicle to tun, and taking a cable off while it is running is potentially dangerous to you and to the vehicle. You can damage the computer and certain electronic components by doing that, including the alternator.

How do you know the alternator is not working? Did you measure voltage at the battery with the vehicle off and the with the vehicle running? The difference should be a volt or two, dependeing on the ambient temperature and condition of the battery.

probly your alternator. at real high rpm it may still charge but not at low. also my be the battery it wont hold a charge then the alternator is trying to power everything at low rpm. then u drop to low and stop charging enough and the coil or fuel pump havnt enough power. if you use a volt meter and watch it. u should have 13 or more all the time and not morethen 15.5 if its working then probly the battery. another posibility is both check ur battery cables. corrosion can cause it to not charge. also make sure ur headlights arnt on because thats putting more on the altornator

check voltage regulator

We had similiar issue last year with my sons 2000 jeep-
diagnosised crank shaft sensor ( repair code 320)- $79.00 part/$75.00 labor. Hope that helps.

First: Are your Battery Cables (inside) and Battery Post nice and shiney? It is amazing how corroded/oxidized cables and post will kill a battery. Get then bright and shiney.
To test the Alternator. Start the Vehicle. You can Jump it if you have to. With the Engine running, disconnect the Negative Cable from the Battery. If the Engine dies, it is a bad alternator.
Was the "new" Alternator new or remanufactured?
Was it the correct alternator inespecially 'amps' for your particular vehicle?
Take the "new" alternator off and have it tested at auto parts store where you bought it.
Any remanufactured alternator may pass the factory inspection but will fail at the auto parts store. Just because it came out of a new box, and looks new, doesn't mean it works new.
Always when buying and part with a "motor" attached to it from an autoparts store, insist that the new one gets bench tested.
If this does not fix the problem:
Are your belts slipping? Worm out, loose or slipping belts will not turn the alternator pulley correctly and draw the battery dead.
Inspect the Red Positive Wire coming off the Alternator back to the battery. Look for any burnt, melted, or shorted areas.
The Battery Starts the vehicle. The Alternator runs the engine and trickle charges the battery.
Let me know if this helped, or if you have addtional information or questions. Feel free to contact me at FixYa.com!

bad cell in the battery won't hold the charge, also check alternator, once the engine is running the alternator should keep it running even with a bad battery, chances are the fouled alternator caused your battery to fail also

Make sure all connections at alternator are attached. On some, the regulator is inside the computer and if bad, requires computer change.

Replace the battery and check the charging system after replacing battery.

Check the Belt Tensioner. If the Tensioner is not Keeping the Belt Tight it will Drain the Battery Pretty Fast.Please Rate my Response, I need all the Help That I can Get! Thanks!