If your MacBook is truly a 2007 MacBook, internet recovery is NOT available to you, it is too old. Internet recovery cannot work on any Mac older than 2010.
So, Option-Command-R does nothing on a 2007 MacBook (and you might be getting a shutdown because of a hardware failure of some kind --- maybe the hard drive is failing.
If you remove the battery, you should see a label inside that battery compartment with the serial number.
If the label inside the battery compartment is missing - can you boot to the Macbook at all? Then you can find the serial number in About This Mac, under the Apple menu. Serial Number should be listed on that information window.
AND -- Apple support won't help you, other than very basic questions, as a 2007 Macbook is considered obsolete.