Dying Tulips

I've just moved and now have a garden for the first time.
The garden was already full of plants when I moved, but the Tulips the
were growing are now dying.They were erect then they started to fall
over, the heads then started to grow upwards again although the stems
were still laying almost flat.

Could this be caused by the fact it has been very wet lately with little
sunshine, except for about 1 week of very good weather?

And what should I be doing to save the Tulips?