99 Blazer starting issues and error code PO753

Sometimes my daughters '99 Blazer won't start. It turns over fine, it just doesn't start. The only error code that ever shows up is PO735. I can reset the code and sometime later the vehicle will start just fine. Can this error code about a shift solenoid have anything to do with the starting issue? By the way where is this shift solenoid located? If this in no way can be a part of the starting, or lack there of issue, do I need to replace this solenoid even though the transmission seems to shift just fine? Any thoughts on why it won't start every few weeks, and then sometime later, starts like there was never a problem would be most greatly appreciated.

What engine and mileage?
How is the tune up end and history?
Transmission ever been serviced?

Codes do not say replace the part.
Code 735 is more of a electrical ciruit problem to the solenoid.

Get the repair flow chart for that code and check out the wiring circuit.

Does the no start and code come on at the same time?

On the no start a good fuel pressure check when no start is first step.
The only true test on a fuel pump is to check the direct fuel pressure from fuel pump.
A quick test is to block off the return line and see if fuel pressure comes up to 75-85 lbs.
But do not run the pump at full pressure very long.
Also when testing fuel pump and pressure you need to tape a gauge to outside windshield or outside mirror and drive it on the road for 20 -30 minutes
until the pump gets has run a while to check for a pump fading out after hot.

Hard to start cold or hot and fuel pressure testing guide lines.
Check cold start fuel pressure.
Check engine running fuel pressure.
Check engine running on the road fuel pressure.
Then shut it off and watch for fast leak down.
Pinch off at rubber part or block off return line and check full pressure.
If pump has full pressure with return line blocked and low pressure without it blocked most usually the fuel pressure regulator is leaking or not holding pressure.
Later V6 and V8 gm engines should have 60-66 fuel pressure.
Cold start should be 64-65 lbs of pressure.
If you do not have full fuel pressure on a cold start the injectors will not squirt fuel.
Do not leave home without it.
Engine running should be 60-66 lbs pressure depending on engine load.
Full pressure with return pinched off should be 75-85 or more.
And if it has a fast leak down after shut off you have a leak in system.
Post back fuel pressure readings.

Ok, I don't have a fuel pressure gauge handy, but I guess I can track one down if need be. My manual says that I can activate the fuel pump by jumping a "red wire in the drivers side corner of the engine compartment, the the positive side of the battery". That sounds like a good test to see if there is a loss of power someplace to the pump, or if when jumped the pump doesn't run, then one can move closer to assuming the pump its self has failed. But, this "RED" wire??? is it the red wire in a 7 wire connector in that drivers corner, or is it a stand alone wire that so far I haven't been able to find????

You need a good gauge to test the pump.
Check pressure and post back readings.
Some parts places sell or rent or loan gauges.
If you find the red prime wire try jumping it.
If not find the pump relay and jumper the gray wire to fuel pump.