Esp driving we slide all over the place on slippery road conditions esp does not seem to be working what could be wrong

Location not stated, or road conditions. nor if in 4low , nor if the ESP switch is off or on. Ask Suzuki for help (lol) or any ASE shop.

it's not magic, it can not give traction , if none.
on ice slow down. (esp can do that too. slow you,brake you and even
shift gears in the transmission)

are you in 4wd? or high 4Low, esp is inactive. (or limited)
read the operators guide. (if lost, get one now)
read the page on driving on ice.
chapters 5,6,7.
have you had any off these conditions , related to ESP, this a
is the ESP light acting wrong, or CEL check engine light running?
are all dash lamps (warning) showing correctly per the opr. guide?
ESP & ABS are vary complex, (not magic)


quote from the servise manual. (car battery dead or disconnected?)
ESP control module
When ESP control module is removed / installed, do
not use impact wrenches which generate shock or
impact to avoid damaging sensors in ESP control
module.
Note that Calibrate word here..!
When any of the following operation is done, calibrate
steering angle sensor, G sensor and master cylinder
pressure sensor (in ESP control module) referring to
"Sensor Calibration in Section 4F
- When battery or dome fuse is removed. (a low battery or weak)
- When steering angle sensor is replaced.
- When ESP control module is removed.
- When yaw rate / G sensor assembly is removed.


read this, it covers this system well,

http://www.wkjeeps.com/wk_esp.htm

read page 7-2 here (the do not drive words)
http://www.autodealertools.com/quickQuote/manuals/2007/Grand%20Vitara.pdf

this car has no center differential. (read limits there of)
are you using chains on the tires?
oper guide page 4-6 , read that yet?

If the vehicle speed is greater thanapproximately 30 km/h (19 mph), the ESP systems (other than ABS) will turn
on automatically and the light will go out.
• When the transfer switch (if equipped) is
turned to the "4L LOCK" position, the
ESP systems (other than ABS) will be canceled automatically. The light will come on and stay on.
• If the ESP systems operate continu-ously such as when driving on slippery roads, the traction control functions of the ESP systems may be canceled temporarily to avoid overheating the brake pads, and the light will come on. After a short period of time, the ESP.

(this latter cut out happens, with wild driving)