I've never dealt with Taurus nor have I owned one, but your request doesn't seem unreasonable. I'm wondering if you talked with someone who couldn't find the information or just didn't want to go to the trouble to find it. I'd call them back and see if you talk to someone different this time - or request to talk to a supervisor. Explain your problem and see what the reply is on your second call. If they still blow you off, then I'd just politely say that you THOUGHT Taurus, especially as a manufacturer in the U.S. was a reputable company that offered Taurus owners good service. In fact, you were thinking of buying another one but all of this has changed you mind.
Irregardless of what some folks think of Taurus, there are a lot of happy Taurus owners out there. If they don't make or have the part available anymore - that would be one thing. If heir records are that sloppy that they can't find your serial # or offer to help you out if you eiher send them a JPEG of the pistol and part or even the part so they could match it . . . I'd say their CS is lacking.
If you don't get anywhere with them, then you might want to post in some gun board classifieds a WTB or "Part Needed" along with a photo of your pistol and the part you are seeking.
Good luck to you - I hope it works out for you so you can get your pistol back together and working.
The the OP, I hope you have more time than money, and also a back up gun if you feel the need be.