If the battery voltage gets down to around 9 volts or less the car may not run. The electrical system must have 9 volts or more to operate correctly. You probably need to get someone to test the alternator and charging system. You may very well have a new bad alternator
The inputs to the alternator should be checked for proper voltage signal. You may need a qualified technician to look at the charging system on your 2000 Cadillac Catera to correctly diagnose your problem.