I have a 1999 BMW 323I five speed, but when ever I shift to 3rd gear the asc light comes on and the car will not pick up speed

Sticks shifts, that I love. for 50 year driving.
and restoring cars.
22 years old and can be repaired
not sure me if gear shift is direct to box or crazy cable drive.?
sure cable snapped.
if it is really in gear,
the clutch blown up, disk now just rivets no friction face there.
or PP pressure plate collapse.

if the MC/slave fails the clutch locks up sold.
yours is opposite ,it slips or shifter is bad (actual)
seem this box has remove ( to rear far) shift linkage
one must be sure this link works and not pull the box only too find out the link is dead, for simple reasons. bad link.
it looks like and old vw bug shifter, (1968 mine) but in reverse.
and vastly shorted link

see this photo.

arrow left pin broke or all parts on the right. bad,
all these parts go to the internal shift rails and forks.

traction control (asc) doesn't work anymore. probably a wheel speed sensor.

try getting the 2-3 shift solenoid from your local auto parts store. that's usually the case when it won't shift into 3rd gear.

BMW 550i hood stuck on right side how to open

just like a computer...you shut if off and turn it on and everything is ok. It's the ABS/ASC control module btw.

replace clutch master slave cylinder.

The ASC light comes on when the system is operating. Ease off on the go pedal a bit on corners.

ive heard people say that on a auto transmission on a BMW that if it wont go into reverse there might be something wrong with the transmission... just a thought, i might be wrong

Check to see if your brake pads and rotors are in good condition. Or if you have replaced the pads yourself and have not reset the wheel sensors this would cause the ABS Antilock Brake System light and the ASC Automatic Stability Control light to stay on as the ASC uses the ABS brakes with computer assistance to control the car

Have your prop shaft bearing check