It is extremely unlikely that all three sockets suddenly deformed
enough
so that light bulbs won't connect to their contacts properly.

Most likely your "tester" is responding to a miniscule amount of current
coupled to it via interwire capacitance. But, that path will not support
enough current to light any kind of incandescent bulb.

You have an open circuit somewhere between your breaker panel (or fusebox)
and the light fixture.

Since the switch is probably near the fixture, and you tell us that it has
to be turned on to make the "tester" lightup/make noise, this tells me
that the open circuit is most likely in the neutral lead, and probably a
fair distance from the fixture.

I'm afraid you're goiung to have to get a professional, or at least
someone quite familiar with these sorts of problems in building wiring, to
find and fix the problem for you.

Good luck, and let us know what it turns out to be,

Jeff

This is weird...have exactly the same problem and discussed it with an
electrician friend of mine earlier tonight. He gave me the exact same
answer you did. I had to check to make sure I hadn't written the original
post.
Tom.