I didn't mess with the firewall, as it didn't occur to me that it would block DHCP. [can it?]
Yes - it is definitely possible, uncommon, but possible. Any service or protocol must use a specific channel or port to communicate. RDP 3398, SMTP 110 etc etc

DHCP, Netbios communication and even ping require a port to utilise. Blocking this port will prevent the service or protocol from working.