Did you run Disk Utility First Aid on the drive when you booted the USB installer?
If you have the non-Retina model, then maybe the hard drive cable is defective. The hard drive cable has an extremely high failure rate on the 13" model, but other models can be affected as well. Or perhaps the hard drive is failing.
Assuming a non-Retina model:
If you remove the drive and boot it externally using an USB to SATA Adapter, dock, or enclosure and it boots fine, then the internal hard drive cable needs to be replaced. Otherwise you either have a failing drive, a corrupt file system, or some other software issue. Booting into Safe Mode can help identify and eliminate some software issues.