Check For Pumps(?)
Hi Scott:
Don't know about a Pearson 27 but on my Pearson 31-2 there is a hand pump in the galley for draining the ice box - apparently, standard/pretty common for Pearsons of various sizes. It is a little straight chromed tube with a tiny spout and a squared black plastic plunger-type pump handle. If you have this, too, try pumping for a while, as it may be dry/clogged/unprimed. I actually had to take a small tube and stick it in the ice box drain and blow through - all kinds of nasty gunk came through the pump into the galley sink. Since then, I have disassembled the pump, cleaned and greased it and it works like a charrm. See if you have one, too. If not, there may just be a hose draining into your bilge (unlikely with Pearsons, though) and the hose may just be clogged.
As for the shower drain in the head, my boat (and, again, seems common on Pearsons) has a sump pump that is toggle switch-activated. See if you can find the switch; it may need to be checked and/or repaired (someone previously disconnected mine - reconnected, cleaned, etc. and it, too works fine). There's probably also a drain through-hull with a seacock on it - look around and see if you can find it; it may just be closed.
Best of luck.
Quint