First off im going to assume that you actually checked to see if the coolant was flowing when the engine was under load. Easy way to check if you havent, is to let your car cool down a bit, and start the engine when it has. The pump runs whenever the the throttle is pressed upon. Therefore just pull the throttle a bit and if the fluid dosent start swirling about then YES your pump has died...then again you would notice when your pump dies since it makes a very irratting whine noise......
Anywho if your pump is working good at this point then your probably getting the code because your level sensor is broken. It happens more often that you think.
From here you can either replace the sensor, OR disconnect the sensor from the wire harness and bridge the end of the connector (wire harness side) within itself.
If your pump is dead you can rebuild it also by just replacing the bearings...
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>Maintenance - Servicing the Intercooler Pump
This is applicable to Water/Air intercooled vehicles (ST165, ST185RC, ST205).
When your pump becomes noisy it may be time to change its bearings. This is a very cheap operation compared to buying a new pump. The pump is located at the front of the car under the battery. To reach it you have to work from under the car.
To remove the pump, you first need to disconnect the the two water hoses and then to unscrew the four nuts and bolts fixing it to your Celica body. Next, unscrew the two round-headed screws you will find at the back of the pump.
Remove the pump itself. You can now unscrew S5 to extract the stator. You just need now to change the bearings B1 and B2. You can get bearings from any bearing manufacturer, but if you want to order them from Toyota the bearing references are 629ZZ for B1, and 609ZZ for B2.
Before reassembling the engine don't forget to unscrew S3 and S4 in the way to extract the carbon contacts. Intercooler Pump Back
Intercooler Pump Side
Info is taken from gt4dc.co.uk...
There is also a step by step PICTURE guide on gt4oc.net.
