Can't set access privileges in 10.4.11

I want to delete a file by dragging it to the trash but I get an error message about lacking access rights.

Sequence:

I highlight the file and try to drag it to trash.
I get this error: You do not have access privileges.
I highlight the file; Then, click on File, Get Info
I go to Ownership and Permissions.
I see: You can read and write - but read and write is grayed out.
I go to the "Owner name", and unlock the padlock.
Under Owner's name, which is DEFINITELY an admin account, I see:
<Access:> Then grayed out, <Read and Write.> I can not get it to un-gray itself.

To make double, triple sure, that "Owner" is an admin account, I go to <System Preferences> and sure enough, beside the owner's name, it says,
Admin.

Besides I used this account to upgrade this lovable old iMac G3 all the way from OS 9.x to OS 10.4.11 successfully. Tiger works fine in all respects. So I KNOW that I'm logging in as an admin.

I even tried opening a terminal window and typing rm <path/filename>.
Result: Permission denied.

Pulling my hair out on this one.

Much obliged for any help.

Thanks,
Tom

What file is this? It sounds like a system file, in which case you can't trash it without wrecking your OS.
If it's not, open disk utility and verify/repair all your permissions, and try again.