A fluorescent bulb was improperly removed from its sockets. I am unable to turn the contact rings from the closed to the open position. I would be thankful for any advice.
Those black pieces are meant to turn 360 degrees in any direction. You already have a key to turn them, in the form of a fluorescent tube. Keep the tube as close as possible to its proper position (i.e. don't try to do this at much of an angle). Turn off fixture power.
Worse come to worst, if you break the lampholder (aka tombstone) or if that type just annoys you (they annoy me), new lampholders are fairly standard, common and cheap. I typically pay 60 cents each for them and keep a bagful on hand. You can mix and match types though I prefer to keep "circular" types separate from "v" types. Height is also a factor, they come in 3 heights. Yours looks like a medium. You don't want a short but a long will probably suffice.