What cause the battry light to stay on when driving?

How old is the battery?

does it stay on when you have driven the car for a few minutes? if you did not drive it , try that

Depending on the vehicle (you didn't include that info) the voltage regulator may be independent of the alternator - check it out as it may be defective.

There needs to be sufficient tension on the "fan belt" driving the alternator - if it slips - the output of the alternator will be reduced.

Check for blown large value amperage fuse(s). These are often found on the under-hood fuse boxes. Replace if blown.

Check wiring. Make sure wires are not cut or shorted. Any connector(s) between the wiring harness and alternator would need to be "100%" as well.

If none of these suggestions solve the problem - repost the question but include the year, make and model of your car / truck.

I would try the regulator, there is a few tests to see if the alternator is charging, use a multi meter and check the b post on the alternator and earth and see what voltage it is producing, check all those sort of things and you will find the problem, make sure the battery terminals are very clean or they won't accept charge as well, hope this helps

You my need to have the alternator looked at again to see if it's charging you also have to look at the fuse for the alternator it may be blown. Also check the check the plug that goes to the back of the alternator make sure it is in all the way.

There are two things that generally cause a battery warning after an alternator replacement. The most common is a loose connection either with the control plug (aka “relay” plug-in), charging line connection, or the ground. The other is a blown fuse or defective connector or relay, which could have been broken or shorted when the alternator was installed or on the first start-up after its installation.
You can check that the alternator is supplying enough power by starting the car and disconnecting the battery. If the car dies, the alternator isn't working properly (or a wiring/relay/fuse issue).

You mean the shifter is stuck?, in park?or the shifter goes to each gear but the car wont move? If the shifter is stuck, check all fuses and be sure the brake lights operate.

disconnect the neg batt cable and bridge it with a test light, it should light up and dim after a few seconds, if it stays bright you have a short in one or more circuits, pull each fuse one at a time to see if you can locate which circuit, good luck

The FuseLink is blown. It is a 100 AMP in-line fuse on the red wire from the alternator.

Have you checked the alternator fuse? The regulator needs power from the fuse to turn on the alternator. The old alternator could have blown the fuse.