If the WinPE boot image loads, but just instantly reboots (quits) after loading. You need to take the SMSTS.log from the Hyper-V PC (press F8 when it boots to get a CMD and prevent it from shutting down again).
If F8 doesn't bring up the CMD, it's because you haven't checkmarked "Enabled command support (testing only)" on the customization tab for you boot image. You need to update the boot image, redistribute it and make new media's too (ISO etc.).
The SMSTS.log is found at: x:\windows\temp\SMSTSlog\smsts.log
This should give you a heads up to what's wrong to begin with. Most likely just missing the driver to the network card? Do an IPCONFIG with the command prompt in PE (F8).
(not likely, but: If the error 0x8007ee7 is present its likely because there’s no DNS server added to DHCP scope.)
I don't know what's the cause of the main problem, but maybe the you can find out by starting with the WinPE issue and get more clues from the SMSTS log file.
Good luck