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From what you wrote so far it seems like you are on the right track to debug this. Opening the boot.php URL in a browser is a good start to try and find out what’s wrong. Are those two computers in the same network subnet? Is the FOG in the same subnet as well? Just asking if there might be a firewall between the booting client and your FOG server.
As well, can you copy&paste the whole output you get in the browser when opening the URL? Just wanna make sure it returns the correct iPXE command codes.
Try opening the URL including the MAC address parameter as well: http://x.x.x.x/fog/service/ipxe/boot.php?mac=aa:bb:cc:dd:ee:ff (copy & paste the output of that here in the forum as well just to make sure this is correct too)