The rule that one should use "I" whenever the first person is in the subject role is incorrect.
The correct rule is that "me" becomes "I" when the "me" is the subject node all by itself. If it is part of a clause that contains other things, and this clause is the subject, then the "I" is supposed to be "me", and it is an illiterate hypercorrection to use "I".
So the following sentence is the correct one:
- Me and Bill worked 'til 4
This one is wrong
The reason is that "I and Bill" is the subject, and the first person descriptor "I/me" is happening at a level lower than the subject. The subject is a conglomeration. When the subject is an agglomeration including "I", then "I" becomes "me". This rule is consistent, and allows for easier transformations, since the whole clause "me and Bill" can be moved to a subject as a unit without having to muck around in the interior, scanning to find the "I's" and changing them to "me's"
- Jack, Bill, me, Harry, and Jane worked late. We asked the guard to open the door.
- Who did the guard open the door for?
- For Jack, Bill, me, Harry and Jane.
No internal scan required to objectify the list. It's already an object. Nobody likes to be forced to scan inside a lexical unit.
Unfortunately, the hypercorrection "Bill and I work late", has been floating around for a long time, so that it starts to sound ok too. To see that
is not grammatical, just reverse the order;
This version sounds like ungrammatical nonsense to any speaker of English. This is very strange, since the order should not matter at all.
- "Me,Jane and Bob are happy to work here."
- "I, Jane and Bob are happy to work here."
The second again sounds like garbage. The reason is that the construction "Bill and I worked late" has been forced down children's throats, so they accept it now, although it is, and always was, ungrammatical nonsense in English.