Hey, just a quick heads-up. BCM943142Y is actually the model number for the Broadcom Wi-Fi card inside the laptop, not the laptop itself. Worth knowing in case this ends up being a driver problem down the line.
From what you've described, it sounds like you're dealing with two separate issues that just happened to show up around the same time.
The first one, your laptop dying the moment you unplug it, is almost certainly a battery problem. A factory reset can't physically harm a battery, so the timing is probably just a coincidence. If it shuts off instantly without power, the battery likely needs to be replaced.
The second issue, the constant blue screen loop, is a bit more involved. When a system gets stuck restarting after a factory reset, it usually comes down to a corrupted Windows installation, a failing hard drive, a driver conflict, or sometimes unstable RAM. Older laptops in particular are prone to hard drive issues.
Here's what to try first: shut the laptop off completely, then turn it back on and keep tapping F11 right away. That should bring up HP's recovery menu. From there, go to Troubleshoot, then Advanced Options, and try Startup Repair. If that doesn't fix it, go back and try System Restore if it's available.
If neither of those work, your best bet is to grab another computer, create a Windows installation USB, and do a clean reinstall from scratch. If even that fails or you start seeing disk related errors, the hard drive itself is probably dying and will need to be swapped out, which is pretty common on older HP laptops that came with mechanical drives.