Any Physics classes, or Electrical Engineering classes where you're a student?
Some OJT (On the Job Training) or "Community College" level suggestions:
1) Get a DMM (Digital Multimeter); $7 is ALL you need to spend. If you haven't used one before, just download the pdf manual and read the parts about measuring DC Volts and Ohms resistance:
https://www.harborfreight.com/7-func...g_q=multimeter
2) Practice measuring Battery Voltage: (a) at the battery posts (the round studs the Battery Terminals connect to), and (b) at the Jumpstart Terminals under the hood.
Post those two Voltage values, and answer these questions:
A) Do you have, or have access to, a battery charger and and extension cord to reach your vehicle? If NOT, do you need instructions on how to REMOVE the battery, either to recharge it or replace it?
B) What is the "Group Size" or "H-size" (H5, H7, etc.) of the battery currently in your vehicle? Copy of take photos of labels on the battery.
C) Do you have, or have access to, a Scan Tool or Code Reader, and if so, the brand & Model of the tool?
I presume when you said "small blue wire" you meant small Blue Connector? That is what you circled in the photo, and that connector connects the IBS (Intelligent Battery Sensor) to the BSD Bus or chassis wiring harness, which allows the IBS to communicate with the DME (Engine Control Module) to regulate charging of the battery. The car will start and run OK WITHOUT:
1) that blue connector being plugged in; or
2) WITHOUT "registering", or any other Web Legend mumbo-jumbo related to the battery.
NOTHING you have mentioned in this thread so far could have "Ruined" your car. You just have a dead battery at the moment. ANY battery that is properly charged should start your engine, so get a battery with > 12.2 Volts charge properly connected to the (+) battery terminal and the (-) battery terminal. Have to be careful removing the battery terminals and the RPDP "Rear Power Distribution Panel" that is located on top of the battery, as improper procedure can damage the IBS, the BST (Battery Safety Terminal) at the (+) terminal, or the RPDP.
You can always TRY recharging your current battery. ALWAYS recharge or JumpStart by applying the power to the Jumpstart Terminals under the Hood, and NOT at the Battery Terminals in the trunk. HOWEVER, if the battery was discharged during freezing weather (for > 1 year) then it's likely damaged internally, requiring replacement.
I would suggest trying to make this a learning experience and NOT beat yourself up. Get a charged battery in there & let us know if you have any problems getting it to crank or fire. ONCE you get it running, post back regarding any needed change of code/option for battery type or capacity.
IF YOU HAVE TO REPLACE the battery, unless you KNOW that it originally came with an AGM battery, I would suggest this H8 Battery from Walmart, $130, and you probably will NOT need to spend time or money coding or "registering" the battery. The Walmart tag on the battery will show the Month/Year sold.
https://www.walmart.com/ip/EverStart...0-CCA/16782659
BTW, the battery you show in the photo is TOO SMALL for your vehicle. That size battery will work for awhile, but is even smaller than an H7 battery. Your vehicle came from the factory with an H8, which completely fills the battery well from front to rear. If you look at your photo, your battery hold-down clamp is on the third threaded hole from rear to front. Smaller battery has less Cranking Amps, AND less capacity.
George