In Disk Utility, you should see your hard drive. The OS X Base System that you see is NOT your hard drive, that is, not your normal system that YOU boot to run your computer. It is the recovery partition. It is quite small, and you are booted to that, so it is working. The 1.3 GB would be accurate - and the files on THAT partition won't help you.
OS X Base System should not be the top item in the drive list in Disk Utility.
There will be a line above named disk1, disk may have another number.
What is above that disk line? You should at least see the name of your hard drive. Original name would be Macintosh HD, but you may have changed the name of your hard drive.
If there are no entries above the "disk1" line, then your boot partition is not visible, probably because it has failed.
You will get to replace your hard drive.
Do you still have the 2007 iMac that you posted about a few months ago? If yes, then you have simply continued to have symptoms which COULD be a failing hard drive, and now it has likely become much worse.
Check again in Disk Utility - if your hard drive is NOT showing in Disk Utility (remember, it has to show the name of the hard drive, which should be the same as what you remember - like Macintosh HD, for example.), then you likely have no choice with your old iMac, except to replace the hard drive.
Just so you understand - the hard drive is where all your pictures, all your music, all you personal files, etc, are stored.
If you have your hard drive backed up (copied) to an external drive, then you will be OK. If you do NOT have your files backed up to another drive, and everything is in your iMac drive, then you might be too late for that...
Let me know what you find out....