Although very old, this thread could be pointing to this problem. 

I had the same kind of DHCP problem. Receiving NAK and WrongServerIDs. 

My solution was quite simple after some head scratching I noticed that the time in the logs was wrong. Somehow the router lost its settings for the date and fell back to 1969 (which is funny, I hadn't seen a time chip reverting to 69 since pre year 2000 bug... usually they roll back to 1900). 

Setting back the time properly and adding IP addresses for the NTP server was the solution. 

Menues: Advanced / System Tools / Time settings. 

Clues: Logs having time difference that made no sence. 

Hard Reset: no

Directly connected to it: yes

Static IP: yes

Model: Archer C3200

WAN mode: DHCP  (no pppoe), behind the ISP own router