Hello -- Heather
The good news is it doesn't look like the recall is for your vehicle. I attached just the top part.
As for your problem. . ..I attached the operation of the fuel system. I think you have injector bleed down. Maybe they are worn out. . ..you do have some good healthy miles on it. To replace them that is about $400 I think just in some parts.
When the key is turned ON with out the engine running, the control module turns a fuel pump relay ON for two seconds. This builds up fuel pressure quickly. If the engine is not started within two seconds, the control module shuts the fuel pump OFF and waits until the engine starts. As soon as the engine is cranked, the control module turns the relay ON and runs the fuel pump. When the engine is cranking or running, the control module receives the Crankshaft Position (CKP) sensor reference pulses which in turn energize the fuel injectors.
You could replace the fuel relay which is about $15.00 and run a can of BG-44K injector cleaner through the engine. I say the relay only because if it is acting up and not coming on correctly you only have 2 seconds then the fuel pump shuts off. The BG will clean the injectors.
Fuel relay location
The only other thing is maybe the Crankshaft sensor. There was a TSB back in 2000 that caused a no start due to bad sensors. You could replace that if you wanted but it they are bad they usually throw a code.
Have you ran by the Zone or O'Reilly's yet for the codes, battery etc yet?
I hate playing let's replace parts since we don't know the exact problem but I am also trying to give you advice on saving the most expensive until last.
Now if that doesn't fix it then you will need to have the injectors tested for bleed down.
I hope this helps.
Recall that doesn't apply to you
MAKE / MODELS: MODEL/BUILD YEARS:
Chevrolet/Suburban 2000-2001
GMC/Yukon XL 2000-2001
MANUFACTURER: General Motors Corp.
NHTSA CAMPAIGN ID NUMBER: 05V155000 RECALL DATE: April 14, 2005
COMPONENT: Fuel System, Gasoline: Delivery: Fuel Pump
POTENTIAL NUMBER OF UNITS AFFECTED: 316508
Technical Service Bulletin on Crank Sensor
Engine - No/Hard/Slow Start/Backfire/Kickback
Notes
File In Section: 06 - Engine/Propulsion System
Bulletin No.: 00-06-04-014
Date: April, 2000
TECHNICAL
Subject:
No, Hard, or Slow Start, Backfire or "Kickback" During
Crank/Start, "Grinding" or Unusual Noises During Crank, DTC P0338
(Replace Crankshaft Position Sensor)
Friday, October 4th, 2019 AT 3:45 PM