Pretty much 100% guaranteed that the (correct) NIC-driver isn't being loaded / associated.
Some NIC's tend to be "difficult" (let's keep it diplomatic) and you may need to hard-bake the driver into the WinPE image. So yeah, it's a driver problem (unless your DHCP is refusing to serve that client for some reason, but a simple Wireshark can verify that).
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Contacting support doesn't cost you anything, assuming you've got a maintenance agreement in place. It wasn't a "cash grab" approach, but rather "hey, in case community folks can't respond, the folks at support usually handle this" matter. That's all.
In case you don't have one with us, and/or with a partner instead, you can reach out to them as well.
But ... I'd be astonished if you're not dealing with a "simple" NIC driver problem. The workaround of "hard" baking that NIC driver into the WinPE image is something that's not new (depends on the NIC's companies use ... some work better, others not so much).
That should hopefully help you .