So you have no Time Machine and no other local backups, and your startup disk is not working? There is no iCloud backup support for Mac, so you’ll be able to recover whatever files were stored there, but not those files kept local to the Mac.
Might be able to get some data off the disk still using Recovery or another boot disk, but that usually means either an expensive recovery, or starting over. Boot Recovery, and try copying your data to another (scratch) disk using Disk Utility.
This situation usually involves a hardware repair to replace what is typically a failing hard disk drive that caused this, or a replacement Mac. Try the Hardware Test; that’ll show some but far from all hardware errors. Given the vintage of this Mac, a replacement hard drive or SSD is certainly possible, but this Mac is already a decade old.
There are recent discussions of a wipe-and-install, though—if the hardware is failing, as is typical in these cases—that won’t work reliably. The Option-Command-R discussed over there will here get you an older OS X version. An iMac 2009-era restore will usually get you either El Capitan or High Sierra, depending on which 2009 model...