The embedded key is hard-coded in the mobo firmware by the OEM on newer PCs sold with Windows pre-installed.
It was an OEM request to MS to avoid the necessity of having to stick a label on every PC individually.
If your PC is old enough to have an external licence sticker then there is no embedded key to find.
If there is an embedded key, then it can't be "wrong". The Neosmart reader is just telling you what the OEM burned into the chip.
If you have installed a different OS to the one supplied with the PC, then the licence key may not be correct for the software you are trying to run.
e.g. if you bought a PC with a "home" edition, then that's what the OEM licence key will allow to run.
An upgrade to "Pro" won't run with the "home" key, because MS expects you to pay for an upgrade.
That's round about the time that W8 came out which iirc was the first to use embedded keys.
Did you buy a PC with W7 or W8 installed ?
Was there (is there still) a sticker on the back with a MS hologram and a serial number ?
What edition of the OS was on the PC ?
Is that still the OS and edition you're trying to activate unsuccessfully ?