1996 Lincoln Cont. Electrical Problem?

Hey everyone...

So I just purchased a '96 Lincoln Continental with 150k miles on it.
I was told that the car had electrical problems and the air ride suspension
was blown, but being a previous owner of a '97 Continental, I couldn't
resist but buying it.

So taking a look at the car, I noticed that the positive and negative
terminals were on the opposite posts of the battery (idiots) :headshake
I purchased a new battery, installed it and started her up.
The car hesitated but eventually fired up.
What I noticed is the battery and ABS light continued to stay on.
The car stayed running for about ten minutes, then everything
started to go haywire.. All the lights in the car were flickering on
and off, the illumination gauges turned off, then the car eventually
shut off.

Thinking it was the alternator, I purchased a new one and installed it.
I started up the car, it stayed running for about five minutes and then
it died out on me again. A "Check Charging System" message came on.

While the car was running, I pulled the negative cable off the battery
and the car shut off.. I JUST put a new alternator in the car...
Could anyone give me an explanation why it would be doing this?

Oh, and one more question. I was told by someone that I could
replace the rear air bag suspension with struts from a '94 Continental.
Is this possible?