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There's the good old sdcards with wifi running Linux that seems like they'd be a good candidate for that.

EDIT: This is the one I was thinking of:

http://haxit.blogspot.com.au/2013/08/hacking-transcend-wifi-...

You can't combine it with power line internet out of nothing - you need an appliance already installed in the first place, and usually the data is encrypted over the power line anyway.

Powerline internet to the fusebox where you turn it into 4G with another device.

You could use UPB to signal over the home wiring to another device.

https://en.wikipedia.org/wiki/Universal_powerline_bus

(Well, I guess there are several different protocols in this area, with their respective transceivers available. I used to use X-10, which has a much lower data rate.)

You'd only be able to get access to the fuse box at a very small company or at a residence. Either of which probably isn't monitoring their wifi or cellular (especially) channels.

You can pick up homeplug signals from other houses if you're on the same phase. And the encryption isn't really the best.

Power line internet is very noisy in the RF spectrum.