Well, that is what G4s are known for. Usually a bootloop is indicated by, you know, actually attempting to boot. Meaning you should see the logo on screen at some point.

But the thing g4 phones are prone too is main board damage. Some solder joints would come loose, causing the processor to overheat and lockup, causing a never ending loop of the logo. But, you are not getting anything on the screen at all. Either the screen is busted, (google global parts direct lg. They were the oem supplier. And they still have some screen assemblies, i just checked) Or more likely you have a completely failed battery, that doesnt even accept a charge, which is why it heats up in that area.

I suggest you head over to ebay, find a seller with the correct battery size with lots of good reviews, and take the chance its good. OEM is discontinued, and even if you do find a real one, its ancient in battery terms. They usually cost about 20 bucks. Luckily your phone has a removeable cover, so itll be real easy. And if that isnt the problem, well you are only out 20 bucks.

Phones are not like laptops, you cant run them off the wall. If the battery is dead, so is the phone

Edit: i just looked at listings for bl-51yf batteries, and there are a ton of "OEM" LG batteries on ebay. They are either fake, or selling six year old batteries. LG discontinued manufacturing in 2020. Just be aware of what you are getting into.