95 buick lesabre custom wont start

Have you checked the fuel pump fuse?

If it starts at all, it probably isn't that fuse, computer or the crank position sensor. On most cars the ignition system gets power two ways. From the switch when in the on or run position and from the starter when in the start position. If it dies as soon as you let the key go from start to run, it may not be getting power in the run position. It could be the switch or wiring, which COULD also be causing the battery drain. The battery drain is because something is getting power when it shouldn't but this could be anything from a trunk or hood light staying on to a power antenna running all the time (which would make a noise) to a bad switch allowing power to something when it shouldn't. Electrical problems are always difficult, good luck.