No Problem,apology accepted!
1st thing!
11.7 volts at key up isn't enough!
C5's require a minimum of 12.5 v at key up or the electronics system won't function properly! A fully charged 12v car battery should carry 12.8-13.2 v,GM's requirements for 97-03 C5's (550 CCA/120 RC) minimum!
Otherwise the column lock actuator may or may not move into the unlock or run position in the column,If you don't hear it at key up,the car will start but will shut the fuel off as soon as it starts moving!
Have the battery charged and load tested,clean and inspect All cable and B+ connections,even the short smaller B+ cable at the power distribution center.
Disassemble,Clean and Inspect All body and chassis grounds,there are several!
(This alone could cure All your problems!)