Turn on computer remotely (internet) and without WOL support

Yes, this is possible.

please note, for this to work the PC bios in question must have options for power recovery.
(i.e. what to do after power is lost. remain off, turn on etc.)

you can use a IP network power switch.

I cant vouch for any, as i have only seen other people implement them. its usually tower based servers, real servers have out of band management for this, in the form of a NIC and embedded GUI so even if the server is hard frozen, you can still shut it down / reboot.

You can find these on Ebay averaging around $50 U.S.

Set the Bios to power on after a power outage, when you leave the house put the switch in the off position via the administrative GUI. Then when you are out on the road or at a hotel etc, when you turn the ip switch back on your computer will power up.

I would think buying a WOL NIC would be the cheaper solution.

Regards,

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

Dell had a DRAC add-in card that you could probably find an equivalent for.

Its a remote management card that has its own IP and etc, but still plugs into the server.

If you were electrically minded you could get something like a raspberry Pi, and mount it inside your case. Every modern computer, is started my momentarily shorting 2 wires together. It wouldn't be terribly hard to connect a transitor between the 2 wires.

Then connect the control leg to the GPIO pin of a raspberry Pi. Then use a python or etc script to momentarily activate the transitor.

There are probably even simplier boards out their than a full raspberry Pi.

Here's one example:

Here's the details

Your pin configuration maybe different, but power and reset have to be there. You could also tap the power and hard drive LEDs as a way to verify it turned on.