Checking a Windows 95 OEM Key for validity
perl -pl -MList::Util=sum, 106 113 bytes

$_=/^(?!000)(([012]\d\d|3([0-5]\d|6[0-5]))(9[5-9]|0[0-3])|366(00|96))-OEM-00(\d{5})-\d{5}$/&amp;&amp;!(sum(split//,$6)%7)


Try it online!

This assumes an ASCII only input. If the input can be outside of ASCII, we'd have to add a single extra byte (a trailing a modifier on the main regexp). It also assumes a leading 366 can only occur in the years 96 and 00, them being leap years. The bulk of the matching is done by a regexp; testing of divisibility by 7 is done outside of it.

Reads keys from STDIN; writes 1 to STDOUT for valid keys, empty lines for invalid keys.

Edit: fixed the issue mentioned by @Dingus.