Engine will not crank over?

Welcome to the forum, my info says the crank relay is located under hood junction box (top). There is also, a pcm/crank fuse, left instrument panel junction block, use a test light on that fuse circuit, goes hot with key in start position. That voltage is crank request to the pcm, then the pcm should ground the coil side of crank relay.

See the guide below, it will help

https://www.2carpros.com/articles/starter-not-working-repair

Wiring diagrams for your starting circuit are attached below

So you have a new fully charged battery?

This guide can help

https://www.2carpros.com/articles/car-battery-load-test

If the security light is on thats why it wont start. Also does the starter work?

You have to be sure the battery has a full charge and the connections are all clean and tight. My next thought is the security system.

Give what I posted a try.

Just because some of the dash lites come on, doesn't mean the battery has a full charge.

Is the security lite on or flashing, when you try to start?

It doesnt need to be running to read codes. You could check for spark actual fuel pressure and for injector pluse.

You can try the 30 minute relearn procedure. When you try to start, leave the key on, watch the security lite, see if it goes off after about 10 minutes, if it does, turn key off for 5 seconds. Repeat the procedure twice more for a total of thirty minutes. If it is going to work, if should work on next key cycle.

You need to check for applicable codes. To check codes, yourself, at the least, you need an obd2 code reader.

Thanks for sharing that with us makes perfect sense I have had plenty of bad bcms cause no starts.

This is a case where unless you know how to do some basic electrical testing you are better off getting a mechanic involved. The generator doesn't even do anything until the engine is running. GM does have a huge problem with theirs but if a jump-start won't help, forget the generator for now. Spark plugs are part of what makes the engine run. You haven't even gotten that far yet if it doesn't crank with the starter.

You can start the diagnosis yourself by visually inspecting all of the battery cable connections and making sure they're clean and tight. That includes where the two cables are bolted to the battery, where the black one is bolted to the engine, and the red one is bolted to the starter. If you use any metal wrench or other tool on the red one, don't let that tool touch anything else metal at the same time. You'll have serious sparks.

Also follow the two smaller battery wires and check those connections. The black negative one bolts to the sheet metal of the body and typically the red positive one bolts to the under-hood fuse box. That last one causes a lot of loose intermittent connections.