Basil Hit with Frost

Help, please!!!
We were hit with frost last night. I have cut down all of the basil, and have set some up with water in ice cube trays. But we have one patch wherein every leaf has taken on dark brown splotches. What would these be, and do they disallow the plant from being edible?

You don't say whether the dark brown spots developed before the frost or after the frost. Most tender large-leaf basils do not tolerate very well night time temperatures below 10 degrees Celsius, so the spots could have developed during cool nights before the frost.
The spotted leaves are not inedible. They may add a touch of bitterness to the flavour, but that is about all. The main objection is cosmetic.

Also, are there other ways to store basil now that it's cut? E.g. freezing, drying, etc.?

You can preserve basil in vinegar or in oil. You can make pesto and freeze that. The books "Herbal Vinegars" and "Herb-flavoured Oils and Butters", available from Richters, are recommended.
To freeze basil, dip clean branches briefly in hot water followed by cold water and then pack in zip lock freezer bags and freeze. Put only as much in a single bag as you would use at one time (because you can refreeze herbs).
To dry basil, be sure to strip the leaves from the stems and dry the leaves in an airy place out of the sun. A sweater dryer (available from Sears) is very handy for drying herbs but do not place leaves on the drier too thickly – in fact the leaves should just barely be in contact with one another. In a few days, the leaves will be dry enough to crumble when squeezed.