Welcome to GMT Nation...
To get you 'Off to a Good Start...' (pun intended) Please visit this next link and Download the GM OEM Full Digital Service Manual (Courtesy
@Mooseman) and follow his Instructions to single out and obtain the one for your Particular SUV. This Reference Guide (PDF) is the Compass necessary to Guide you through the "Crank- No Start" issues and the related "No Start-No Crank" problems bu following the Diagnostic Trees covering these Issues.
Having a Good OBD2 Scanner, a"Scope on A Rope" Lighted Continuity Probe and a Decent Digital Multi-Meter along with a Fully Charged Battery offer much assistance as you to try to run each problem 'To Ground". The Chapters in these REAL Service Manuals make the other "Repair Books" look like Thumb-Nail Sketches on the back of a Party Napkin.
Remember that your 'underhood' Power Distribution Center...with various Fuses and Relays along with the Fuses/Relays with the BCM under the Left Rear Seat are often the Best Places to Check First once you examine their 'undercover' Lids for the #s and Locations of the ones you think are related to the problems:
********* Please note that the FireFox browser has issues with the password handling and that these downloads are not under HTTPS, flagging them as security risks. Chrome and Edge work fine once you allow the download. ********* ATSG 4L60E Manual 4L60E Rebuild Manual 2005 GMC Envoy XUV...
gmtnation.com
These Three Diagrams cover the Ignition-Starter Circuit and the Fuel Pump (Two Separate Diagrams) that can help you with Diagnosing the Circuitry and Components that begins with 'The Turn of The Key"...and everything in between that can go wrong to stop the Engine from Running Right. Please Post ALL of the GM Codes you are able to Read on the OBD2 Scanner ...and Remember to take them in their Order of Appearance to obtain the Best Solutions: