Let's keep reviewing on hardware & software solutions, this is almost the last post on troubleshooting and it gets interesting people!
Troubleshooting a Mac is similar to troubleshooting a PC in most important ways, since the two have shared basically identical internals for the last six years now (and even before the Intel transition, the fundamentals were mostly the same). As such, the symptoms they present will be the same, and some troubleshooting steps (particularly for display and power issues) will be identical. Macs do use their own troubleshooting tools, though, and there are a few Mac-specific troubleshooting steps that the AppleCare representatives are going to ask you to perform when you call in.
Apple’s main diagnostic tool for Macs is the Apple Hardware Test, which ships with all new Macs and has remained nearly unchanged (right down to the OS 9-style windows and buttons) despite the Mac platform’s numerous software and hardware changes over the last decade. The tool can be accessed by holding down the D key at boot, but if you've wiped or replaced your Mac's hard drive since buying it, you'll need to go through a couple of extra steps: on older, pre-Lion Macs, you can find the Apple Hardware Test on one of the restore DVDs that came with the computer. Newer Macs can access the tool via the Internet thanks to the Lion Internet Recovery feature, again by holding down the D key as the computer boots.
Performing the Extended version of the test is recommended, since it’s the one that is more likely to find errors. It will do fairly robust testing on your memory, motherboard ("logic board" in Apple parlance), and other components—take note of any error codes or messages you see while the test is running. Other diagnostic tools (like TechTool Pro) have been developed for the Mac, and Memtest86+ will also work as a memory tester, but for the purposes of getting support, Apple tends to want error codes and messages generated by its own tools.
You can use Disk Utility's verify and repair disk options to check for some hard drive failures—it relies on the SMART self-reporting information from the drive to detect problems. My personal experience with SMART has been a bit mixed—it has detected drive failures in time to save the data, but it has also failed to catch errors before a drive or two became unreadable garbage. As is the case on PCs, a good backup strategy is your best protection against drive failure.
There are also a couple of Mac-specific things you can do to get rid of minor, intermittent problems, especially those related to trouble booting or powering on. Most Apple techs will ask you if you’ve already performed these steps, so even if they don’t fix anything, you might as well try them.
The first such trick to reset your PRAM, which contains settings for virtual memory, the computer’s startup disk, and a few other settings (the entire list is located on Apple’s support page. To reset the PRAM, turn your computer off, press and hold the Command, Option, P and R keys, and power on the computer. Once you hear the startup chime the second time, let go of the keys, and see if your problems persist.
The second Mac-specific fix is to reset the System Management Controller (SMC), which can fix fan speed and power issues (including both the system’s power lights and the ability to power the system on)—a complete list is available on Apple’s support page. On desktops and older MacBooks with removable batteries, resetting the SMC is just a fancy name for power cycling a PC—unplug the system, remove the battery, and hold down the power button for a few seconds to drain any residual power from the system. On newer MacBooks with built-in batteries, you must turn the computer off, then press (but not hold) the Shift, Control, Option, and power buttons at the same time.
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