For help finding your serial number (if your computer does turn on), you can copy & paste your serial number from the Apple System Profiler: under the Apple menu, click "About This Mac"; then, in the window that pops up, click "More Info" — your serial number is in the right-hand pane. If your computer doesn't turn on, Apple has a thorough guide.
If you'd rather not provide your full serial number, we also accept 3-digit or 4-digit model identifiers. If your serial number is 11 digits (pre-2010), the model ID is the last 3 digits; if it's 12 digits, it's the last 4 digits. Please be aware that your full serial numbers are recorded only if we aren't able to match it to a computer, for the sole purpose of adding its model ID to our database, after which it is deleted.