How would I seal the raw edges of particle board cabinets for protection against getting wet?
I've never done this, but certainly I can think of occasions where I have seen this kind of water damage on particle board furniture in kitchens.

I would consider waterproofing it by using a glue that will form a plastic-like layer to cover the exposed edges. PVA will work and is cheap and easy to apply, but isn't very hard wearing. An epoxy resin is a tougher alternative.

A quick Google to back up my intuition gives me:

http://www.diydoctor.org.uk/projects/pvaadhesive.htm

Which states:

"Timber can be sealed with PVA to give it a waterproof quality, although if the surface of the timber is to be subject to any wear or traffic, then PVA, as it is an emulsion, will eventually fail."