No IP address

My Internet has been down at home since April 16, plus I've had intermittent outages all month. Comcast is not responding to DHCP packets. I verified with tcpdump that my router is broadcasting DHCP Discover messages correctly, and Comcast is ignoring them. The physical layer is working fine, and Comcast can still successfully reboot my modem remotely.

Things I've tried: Rebooting the modem and router; restarting my router's DHCP client with tcpdump logging; contacting Comcast over chat; I got escalated with an ER1 ticket; a technician was suppose to call me Sunday but they were a no-show; Comcast's online chat is broken since yesterday and won't let me speak to anyone anymore.

Things I could try: Should I just start assigning myself a static IP address and hope I avoid collisions? I haven't done this yet since this could confuse technicians trying to help.

EDIT: Comcast just assigned me an IP address, for the first time in 4 days. My modem and router setup is still the same. I suspect that my Internet will continue to be intermittent, so I'll come back when it breaks again. Thanks!