Purchase nothing at the moment, I would have the present PSU tested by a reputable tech store who have the required equipment, test the speaker on your system for sure but don't go dismantling it, if the speaker emits a single beep when your MB completes the POST you know that the speaker is good.
I do not wish to alarm you but the attached video is the one that I use as an example to show the sort of equipment that is required to conclusively test a PSU, I am not aware of any Staples outlet for example that has such equipment in store.
What the equipment does is simulate a computer under load and so the PSU behaves as it would when it is powering your PC, multi-meters and the basic testing devices that you can purchase from some merchants only test the basic voltage output from the PSU rails and so cannot be relied on as 100% conclusive.