What is the exact model of your laptop? You can get this information by entering your serial number here:
https://checkcoverage.apple.com/
You need to press the special startup keys at the proper time otherwise those keys will be ignored and either the Mac will do nothing or it will attempt to boot normally (in this case there is no internal boot drive as it has been erased). You need to press the startup keys immediately after hearing the startup chime (within a second maybe two depending on the model). This assumes that there is no hardware issue with either the built-in Keyboard or the Logic Board (every once in a while I come across an Apple laptop that won't properly register the startup keys or registers them incorrectly even if all the keys work fine when booted normally into macOS).
Internet Recovery Mode uses Command + Option + R. After you erased the drive you needed to go back to the utilities screen and selected "Install macOS" or "Reinstall macOS" (the option may be either one of these). If you have access to another Mac that is capable of running an OS your old laptop can run, then you can also create a bootable macOS USB installer using the instructions in this Apple article:
How to create a bootable installer for macOS - Apple Support
FYI, here is an Apple article with instructions on everything you should do when preparing a Mac for sale or recyling:
What to do before you sell, give away, or trade in your Mac - Apple Support