Check engine light comes on

Failure Mode Effects Management (FMEM) is an alternate system strategy in the PCM designed to maintain engine operation if one or more sensor inputs fail.
When a sensor input is perceived to be out-of-limits by the PCM, an alternative strategy is initiated. The PCM substitutes a fixed value and continues to monitor the incorrect sensor input. If the suspect sensor operates within limits, the PCM returns to the normal engine operational strategy.
All FMEM sensors display a sequence error message on the scan tool. The message may or may not be followed by Key On Engine Off or Continuous Memory DTCs when attempting Key On Engine Running Self-Test Mode.
With the fail safe mode was the "Service" wrench light lit or check engine light ?
With

It may be if you ignore the light. Check the oil level and coolant levels first if ok have the fault codes read to determine the sensor that put the light on. Repair it and go from there.. Normally the ECM goes into safe mode to protect the engine and gear box from serious damage but it depends on the driver to react promptly to stop further damage occurring.

safe mode means the computer is protecting the engine by shutting down some operations - like half the cylinders.

go to autozone & have codes read (DTC) free.

I know of no such warning light on the 2006 Chevy Equinox that shows a wrench with an engine. The wrench with an oil can beside it means that there is scheduled maintenance required as listed in your owner's manual. You will see this when it it time to change the oil. The light that shows an engine is the Check Engine light and comes on when there is a problem with the emissions system. It requires that the ECU be scanned with a scan tool to retrieve the code that has been set. A trained professional will use this code to repair the problem.

Follow the steps care fully

Open the hood and relieve the fuel system pressure. On the fuel rail, right before the first fuel injector, locate the Schrader valve-similar to a tire air valve-on the inlet fuel line. Using a small screwdriver, depress the stem inside the valve while covering the valve with a shop rag to catch the squirt of fuel.

Raise the back of the vehicle using a floor jack and support it safely on jack stands.

Locate the fuel filter along the frame rail-passenger side-of the vehicle, near the fuel tank.

Unplug the quick-connect fuel inlet line on the back of the filter by pressing the lock tabs. Push the connector towards the filter and then pull to disconnect the fuel supply line.

Disconnect the outlet fuel line from the filter-the line going toward the engine-by using a backup wrench to hold the line nut while disconnecting the lock nut on the filter with a tube wrench.

Remove the filter from its mounting bracket and install the new filter in place, making sure the arrow on the side of the filter case points toward the engine.

Install the outlet fuel line. Tight the lock nut finger tight, then hold the fuel line nut with the backup wrench and tight the lock nut with the tube wrench. Make sure not to over tighten the nut to prevent fuel leaks.

Press the fuel supply line fitting against the small tube at the back of the filter until the lock tabs snap in place.

Lower the vehicle, start the engine and check for leaks.

its a check engine light possibly an o2 sensor

This would be your engine check light. First off you need to check all your fluid levels. This includes windshield wiper fluid, brake fluid, oil, transmission fluid if it is an automatic. Remember that the transmission fluid on an auotmatic measuers in pints on the dip stick and not quarts even though it comes in quart bottles. The car must be in neutral and riunning while checking the fluid. Be sure you put the emergency brake on too just in case it ever slipped into gear. Things happen. Check radiator water level and power steering fluid.
With this light on it the computer will drop the engine into safe mode and have less power. If after all the fluids are filled and it is still on then it will be time to take it in and have the mechanic check the computer to tell you what needs repaired. This may cost 75 bucks or more but there is a thousand things that can turn that light on. Unless you can tell me if the car was acting up in any other features prior to the light coming on. If so then let me know and I will try to help you, Good Luck, The Raz

Wrench light, is "Service Engine Soon". Check light indicates there is a stored and current engine computer fault. Often referred to as a DTC,,,Detected Trouble Code. Stop by your Autozone or Advance Auto parts store and they can plug in a scanner that will tell what faults occured and possibly what you can do to take care of the problem,

This is actually a very easy fix.
The switch is on the transfer case, you'll see wires or small harness going to it.
It should be the only electrical switch on the transfer case.
It unscrews by using a socket or wrench.

well many vehicle will go into fail safe mode when there is problems with communication between modules or the engine light comes on this prevents the vehicle from damaging its self it will run on pre set parameters to protect its self but i no it doesnt feel that way it can be very harsh the next step would to be pull the codes with a scanner because many codes and problems can cause this