I checked and that mobo does have wifi built in.
The wifi drivers for it are here, download and install the latest version (22.200.0.6).
In case that doesn’t work, open Device Manager and check under Network adapters if there’s something like Intel wireless. If it is present but there’s a yellow exclamation point icon, that means Windows can find it, but it’s not working for some reason – perhaps removing the driver for a reinstall could fix it; get back for further instructions if needed.
Whatever you do, do not turn it on. From what you said, it’s likely already damaged somehow with the internals shorting, which makes the computer turn on and off at random. A trusted computer shop is a must so they clean the insides and diagnose any damage.
I had a water leak in the attic once that percolated through the ceiling exactly over my open laptop, which was off at the moment. I pulled the power cable out and threw the laptop on the couch while I sorted the leak out, but failed to remove the battery – when removable batteries were a common feature.
I got back from the attic and the laptop was on. The keyboard was shot and only worked properly again after I replaced it and the system clock was forever wonky, randomly jumping back in time, which I fixed by installing a program to check a time server every minute and set the clock if needed.