2003 Ford Cobra cooling

Today when I got to a friends home after driving my cobra kinda hard on the way there I noticed it was hot a little to where the coolant was coming out the overflow. Upon further investigation I noticed the fan was not coming on as it should when hot so we put in a new cooling fan relay. Did no good. Fan still didnt work! All the while it had been cooling down while we put in new relay so we decided to straight wire the fan to the battery, well it worked fine then but made rubbing noise like something was caught in it. Upon closer looking I found the layer of watever kind of material that comes around the hoses had somhow came aloose and fot caught in the fan a little. I removed but fan still would not come on properly. I am wondering what would cause this?