rfc 3330...

years ago when i was dumber than i am now i used to refer to host addresses of 169.254.x.x as those stupid windows addresses that are dished out by microsoft when the host can't find a dhcp server...

they are actually dished out by IANA, kind of... 

IANA                         Informational                      [Page 2]

 
RFC 3330               Special-Use IPv4 Addresses         September 2002


   169.254.0.0/16 - This is the "link local" block.  It is allocated for
   communication between hosts on a single link.  Hosts obtain these
   addresses by auto-configuration, such as when a DHCP server may not
   be found.

as soon as you get one of those addresses on a host you think, O MY GOD, the dhcp server is down... that might be... however, and i'm sure you know, you also might be experiencing a connectivity problem in the path to the dhcp server...

and there is also the possibility of not getting the 169.254.x.x address although the dhcp server IS down... that's hardly fair... the client has no reason to broadcast for the address again once it has its lease... of course if you manually try to renew and ipconfig hangs up in the pursuit of a legit address, you've suddenly learned something...

for troubleshooting, before blaming the dhcp device, i vett l2 first...

on the client's switch...

sh int
sh vlan brief
sh int trunk
sh etherchannel summ
sh port-sec
and l3 checks if applicable...

generally speaking, if it's a l2 problem, sh int, sh vlan and sh int trunk will reveal most everything...

then onto the next switch in the path, which should eventually lead to the dhcp server...

granted this next guys link is not necessarily troubleshooting, and he may have some thoughts here that you might consider... however even for discovery purposes, i would not resort to his kind of bullshit below...

https://w.ntwk.cc/initial-ccie-lab-checks/

i am not going to pollute my pages with a sample of his, er, ideas...  go see for yourself...