I Have a problem with my 2000 Galant TCL and Antilock Brake light. They stay on constantly since I had a rear flat tire.

That means there is a problem with the ABS , has DTC'S - diagnostic trouble codes in the EBCM - electronic brake control module . You need to have diagnostics run on it !
Traction Control/ Stabilitrak Off: Refer to ABS Description and Operation in Antilock Brake Systems
This vehicle is equipped with the BOSCH 5.3 antilock braking system.
The vehicle is equipped with the following braking systems:
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Antilock Brake System (ABS)

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Dynamic Rear Proportioning (DRP)

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Traction Control System (ETS) (w/NW7)

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Traction Control System (TCS) (w/NW9)

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Vehicle stability enhancement system (VSES)

time to have the fault codes read . check the fluid level in the brake master reservoir
It means that the ABS system is not working.

There is something wrong with your anti-lock system. That's why the light is staying on, to warn you of a malfunction. Have it serviced.

Make sure your tires are all the same size[did you just put on only two new tires?] . Then check the wheel sensors.Also make sure your tire pressure is perfect!

go to diferential,on center top its posible you find and speed sensor ok if its there,replace it,if it has antilock light on,it has a and antilock sensor problem ok,go to rear axle.

Something as simple as a different tire size can cause the abs to go nuts. I even had it where the two tires were the same size. But a different brand name. Each manufacture has their own tire sizing so not all tires a equal in size. Even though it says on the side of the tire that they are the same size.

Sometimes the cooper inside the insulation of the wires going to the sensors corrodes. Especially on the front units. It reads more ohms than normal but not open and is very intermittent. However moving the wires my make it work for a while. That's why replacing bearings seems to fix the problem but it comes back after a while.

You can test the speed sensors yourself...
Front sensor specs:
956 to 1240 ohms in 41 to 110 degree weather
at least 100mV AC (NOT DC!) volts when hub is spun by hand
Rear sensor specs:
950 to 1300 ohms in 41 to 110 degree weather
At least 100mV AC (NOT DC!) volts when hub is spun by hand

Here is some information from service bulletins that could be related to the problem. The traction control, antilock brakes, and tire inflation monitor all use wheel speed sensor input.

This first bulletin seems like it could be the problem because engine movement is involved:

GM Corporate Bulletin 00-06-04-049B
This Bulletin covers a problem that can cause multiple failures, one of which is an Antilock brake problem, and covers 2000-2003 Impala and Monte Carlo built prior to 2/03.
Check to make sure the wiring harness adjacent to the AC accumulator/dryer is not rubbing against the ac accumulator chaffing through the insulation of the wires in the harness.

GM Corporate Bulletin 03-05-25-008 overview:
GM front wheel speed sensor harness replacement - 2001-2003 Buick Century, Regal; 2001-2003 Chevrolet Impala, Monte Carlo; 2001-2002 Oldsmobile Intrigue; 2001-2004 Pontiac Grand Prix
This bulletin is about inspecting the harness going to the front wheel speed sensor for wear from contact with front suspension parts.
Repair harnesses/leads are available that can be spiced onto the main harness.
2001-2003 impala & Monte Carlo – Right side - 10340313
2001-2003 impala & Monte Carlo – Left side - 10340314

SERVICE BRAKES, HYDRAULIC:ANTILOCK:ABS WARNING LIGHT
• TSB #030525008 -- INTERMITTENT/CONSTANT ANTI-LOCK BRAKING SYSTEM (ABS) MALFUNCTION INDICATOR LAMP (MIL) ILLUMINATED. *TT (NHTSA ID #10004719, OCTOBER 01 2003)

Hope helped.

Hello,
It sounds like the wheel speed sensor may have been damaged in the process of removing the tire. That would cause the abs light to come on. Ususaly when the abs light comes on it is a sign they won't opperate as abs but only as standard hydraulic brakes. I hope this helps. If you have more questions reguarding this or other conserns please ask me. Please remember high ratings are very important to me.

Thank You,
Roy

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

Start with checking the sensors on each wheel.  These will be the electrical wires that come from behind each wheel.  Also check that the tire pressure in each tire is the same.  Next, check your brake fluid level.
Sorry...that's all I can help you with.  Maybe someone else can help you from here.

check your break lines or remove the tires and pull off the brums and look at the automatic adjusters