What system version?
Can you boot to Internet Recovery.... Command - Option - R?
OK try this:
Resetting the SMC & PRAM for Mac Pro, Intel-based iMac, Intel-based Mac mini, or Intel-based Xserve 1. Shut down the computer. 2. Unplug the computer's power cord. 3. Wait fifteen seconds. 4. Attach the computer's power cord. 5. Wait five seconds, then press the power button to turn on the computer. 6. Press and hold the Command-Option-P-R keys before the gray screen appears. 7. Hold the keys down until the computer restarts. 8. Release the keys and try to boot to Recovery HD again
That is very odd I suggest you do a full backup to an external drive using Time Machine and then you will have to take it to Apple or another service provider. There is some kind of hardware failure that is stopping it from booting to Recovery HD which it the one boot partition that should ALWAYS work. We can't diagnose what that is here... they have special network boot diagnostics that can tell you what the problem is but you will need a complete backup they will have to erase the drive.
Sorry but if you can't boot to a recovery partition then there is nothing more you can do on your own. Apple is right I wish there was a different answer but it is what it is. At least you can boot and make a backup many are not so lucky in this situation... single user mode won't help in this situation unfortunately...
If you added any RAM or other hardware that is not what was installed originally you can try putting the original hardware back but that's about it, resetting the SMC and PRAM already cleared out any software issues