Q: how to back up a imac thats won't open

Hi .. I have a imac 27" ..it's about 2010/11 i think ... it's recently had new HD put in, but the screen keeps just freezing so i have to turn on and off, sometimes 5 times a day . today it just won't turn on at all.the light grey screen comes up after doing comand=R ..I then tried the disk utilites reapir but it's says i need to back up before I reinstal everything ..   ...how do i back up a imac that won't open {trying to do disk repair and it's not showing the verfy button at all }.When i did the first aid its says i have to back everything up first and then reinstal.My question is how to back up from this point .. thanks ..hope you can help