Manufacturer = Inter City Furnace
Manufacture Date = 1991
Type = Forced air - up draft (house is on a slab)
Fuel = Nat Gas

The furnace cycles on and off correctly BUT it seems that the blower motor takes a long time to turn on - the flame is burning for maybe a minute(?) before the blower starts.

Is there a setting that has gone out of adjustment? Something I can adjust?

That sounds normal. The gas turns on firdt and heats the furnace then the blower blows the hot air out. If not for a control that does this you would have cold drafts all the time with the blower running without heat.