The Blinking question mark says: I could not find a Bootable source of software isn the place you told me to boot from.
Sometimes if it "just forgot" if you leave it for a while it will look around and find other source. Sometimes (as you said) it is caused by the drive no longer bootable.
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Those (negative low thousands) error codes mean that in some fashion, your current Wi-Fi is inadequate to serve as a basis for Internet Recovery.
Common problems include:
Hidden Network-name
required use of a proxy server to get Internet access
required use of a login page to get Internet access
Use of a login server or certificate to get Internet access
Use of PPPoE in the Mac to get Internet access (typically only applies to DSL)
Use of Fixed IP address rather than good old DHCP
Failure of Router to provide workable DNS server addresses
If you have an Ethernet port, you may in some cases be able to move your Mac close to the Router and connect to the Router using Ethernet.