There are several things you can try that will be quick and are safe.
If during a boot it shows a gray screen see: http://support.apple.com/kb/TS2570
If during a boot it shows a white screen with a question mark see: http://support.apple.com/kb/TS1440
At boot time it is trying to fina a bootable system disk. It could be a failed system disk or several other problems.
Below are step-by-step instructions from one of the experts in this forum (ds store) to diagnost and/or repair you Mac.
This looks like a large, daunting document at first glance (18 pages) but the parts you need to work are actually quite simple. Print it out. You will want a copy of it for now and for future reference whey you might not have access to a live computer. Most of what you need are on pages 4 though 6.
You have two main goals: (1) To get the system running again or to get it running enough to see your data. (2) To secure your data. If you have a recent backup, then the data is secure. If not you will need to copy your data from the internal disk to an external one. For the this you will need a blank external disk. Do not use your Time Machine or other backup disk. Preserve that one.
Once you have the system running again be sure to make two (not just one) backups on two separate external drives. This will help you if you find yourself in an emergency situation again.
Here is a summary of the steps from the document referenced above. If you get stuck on any of the procedures jump to #9 (recovering your data).
First disconnect all external equipment but keep the power supply plugged in. Do not use wireless keyboards or mice for the following tests.
1) SMC Reset (page 4 in the document):
• On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
• Release all the keys and the power button at the same time.
• Press the power button to turn on the computer.
• If it did not boot press and hold the power key for tens seconds to turn on the computer.
2) Zap the PRAM (page 4):
• Locate the following keys on the keyboard: Command, Option, P, and R.
You will need to hold these keys down simultaneously in the next step.
• Turn on the computer.
• As you hear the bong, press and hold the Command-Option-P-R keys.
You must press this key combination before the gray or white screen appears.
• Hold the keys down until the computer restarts and you hear the startup bong for the second time.
• Release the keys.
3) Run hardware diagnostics (page 5):
• Read step 3 in the manual. It gives additional instructions not included here.
• In this next step you will need to be patient as it does runs a diagnostic on your hardware.
This will test can take minutes.
• Press the power button and as you hear the bong, hold down the D key.
• Be patient. Hold down the D key until something happens other than the gray or white screen or for up to two minutes.
• After your computer restarts, you may see the Apple Hardware Test chooser screen.
On my computer it simply reboots normally after it waits a long time, but then my Mac is older and not sick.
• If you don’t see the Apple Hardware Test chooser, Apple Hardware Test may not be available on your computer.
• When the Apple Hardware Test chooser screen appears, select the language you want to use,
and then press the Return key or click the right arrow button.
• When the Apple Hardware Test main screen appears (after about 45 seconds), follow the onscreen instructions.
• If it gives you any diagnostic codes, write them down, check what the mean on page 5, stop testing and report back.
• Proceed to step 4 no matter what diagnostics you see or don't see.
4) Startup manager (page 5):
This step will try to boot from a recovery partition on your hard disk. If it boots that is a good sign.
• Press the power button and as you hear the bong, then hold down the alt/option key.
• If it does not boot report back. It is time to take it to an Apple store.
It may have a failed disk or some other hardware problem.
This does not necessarily mean the data on your disk is gone. That may still be recoverable.
5) Disk Utility (page 6):
If you have gotten this far that is a good sign.
This step will check the the filesystem integrity of your internal disk or SSD.
It is time to refer to the instructions in the large document I referred to yesterday.
• Follow step 5.
• You will start by repeating step 4 (power then option key) and then run the Disk Utility.
• If it won't boot that way then try a network boot (power then command-option-R keys) and then run the Disk Utility.
• Report back with the results.
Continue progressing through the steps in the manual. If you get stuck remember to jump to #9 and try to recover your data.
Good luck. I hope to hear good news from you soon.
If you need to take it to an Apple store or Apple Authorized Service Provider, take your most recent backup disk and a blank disk with you. If it is less than a year old or covered by AppleCare+ they will repair it for you for free. Otherwise they will diagnose it for free and give you a repair estimate.