iMac 27" Snow Leopard 10.6.8 Problems turning on Time Machine

iMac 27" running Snow Leopard 10.6.8 purchased 2011. Had to have Apple replace the system card after about a year. Everything working fine. I had a new Seagate back up drive installed still working as far as I know but I can't turn on Time Machine. It keep turning it's self off for some known reason. I really want to use it to see if it has been backing things up automatically but I don't know how. I'm afraid I might erase information that might be there. Is it possible that my portable Seagate Back up Drive is storing all the info that should be going to Time Machine? I looked at my all my Hard Disks and none of them are Labeled Seagate or external back up. Any one have a clue here? This is my first post so I hope someone with experienced with Snow Leopard, Time Machine on iMac and will respond. I haven't heard one positive thing about switching over to El Capitan have you?

Thanks so much!