the delay relay has nothing to do with the fan if its not working ,
you can unplug the relay and toss it in the trunk and the fan will still work as the should , the delay relay wont be the cause for the fan not turning on , it generally fails and keeps the fan running which drains the battery
try the low speed fan relay which is the smaller relay next to the delay relay
even if the relay for low was bad the fan would still come on at 200 degrees or so because the overheat switch would turn on the high speed relay
try supplying 12 v to the fan and see if it works