Hey Derek, the pin code issue when pairing AirPods with Windows 10 is pretty common. The thing is, AirPods do not actually use a pin code for Bluetooth pairing, so the 0000 and 1234 you tried would not work because they are not the right codes for AirPods.
Here is what you need to do:
First, make sure the AirPods are in pairing mode. Put them in the case, open the lid, and press and hold the setup button on the back of the case until the status light flashes white. This puts them in pairing mode.
Second, on your Windows 10 desktop, go to Settings, then Devices, then Bluetooth and other devices. If your AirPods are already listed there, click on them and choose Remove Device. Then click Add Bluetooth or other device and select Bluetooth. Your AirPods should show up in the list.
When Windows asks for a pin, try just clicking Pair or Connect without entering anything. Sometimes the pin prompt is just a generic Windows message and you can skip it.
If that does not work, try entering the code 8888 or 000000 as those are sometimes accepted by Windows for Bluetooth audio devices.
Another thing to check is whether you have any third party Bluetooth software installed on your PC that might be interfering. If you do, try disabling it temporarily.
Also, make sure your Windows 10 is fully updated, as older versions of Windows can have Bluetooth driver issues that cause pairing problems.
If none of these steps work, you could try pairing the AirPods with your phone first, then forgetting them from the phone, and trying the Windows pairing again from scratch.
Let us know how it goes!