well i would start out by starting the car when its cold and take off the reservoir cap and watch to see if you can see the water move in that, if you can see it move that means the water pump is working. If that checks out ok i would take out your radiator and flush that out really well, while that is out just buy a good thermostat and put that in anyways its cheap and its a good thing to do anyways. While you are this far into give your radiator hoses and clams a good looking over and make sure those do not need replaced. Then put fresh new coolant in that and make sure you bleed out the system really well. Now on the 02-03 i know there isnt a radiator cap on the radiator so i always filled the coolant threw the upper hose then put that back on then filled the rest with the top reservoir. Try that and let us know how that works. If it's a water pump they are not that hard to put just takes some time.