MBP Requires Two Attempts To Startup

Question

My wife's MBP 2.4 GHz Core 2 Duo OS 10.5.8 takes two attempts to startup at least 50% of the time. She thinks that the problem started around six months ago. It stalls at the white startup screen. Clicking the power button turns it off and then it invariably works fine the second time the power button is clicked.
The MBP is not connected to any peripheral devices and I cannot associate the start of the problem with an update or software installation. The MBP is essentially identical to our 24" iMac in terms of installed programs and its configuration. The iMac occasionally has the same problem but it is much less frequent in nature, perhaps one out of every 50 times it is booted up.
I could use some help diagnosing the source of the problem. If it may be a hardware-related problem I would like to know because the extended AppleCare warranty is up in October.

Answer 1

I would just reinstall OS X as follows:
How to Perform an Archive and Install
An Archive and Install will NOT erase your hard drive, but you must have sufficient free space for a second OS X installation which could be from 3-9 GBs depending upon the version of OS X and selected installation options. The free space requirement is over and above normal free space requirements which should be at least 6-10 GBs. Read all the linked references carefully before proceeding.
1. Be sure to use Disk Utility first to repair the disk before performing the Archive and Install.
Repairing the Hard Drive and Permissions
Boot from your OS X Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Installer menu (Utilities menu for Tiger, Leopard or Snow Leopard.) After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer. Now restart normally.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
2. Do not proceed with an Archive and Install if DU reports errors it cannot fix. In that case use Disk Warrior and/or TechTool Pro to repair the hard drive. If neither can repair the drive, then you will have to erase the drive and reinstall from scratch.
3. Boot from your OS X Installer disc. After the installer loads select your language and click on the Continue button. When you reach the screen to select a destination drive click once on the destination drive then click on the Option button. Select the Archive and Install option. You have an option to preserve users and network preferences. Only select this option if you are sure you have no corrupted files in your user accounts. Otherwise leave this option unchecked. Click on the OK button and continue with the OS X Installation.
4. Upon completion of the Archive and Install you will have a Previous System Folder in the root directory. You should retain the PSF until you are sure you do not need to manually transfer any items from the PSF to your newly installed system.
5. After moving any items you want to keep from the PSF you should delete it. You can back it up if you prefer, but you must delete it from the hard drive.
6. You can now download a Combo Updater directly from Apple's download site to update your new system to the desired version as well as install any security or other updates. You can also do this using Software Update.