You've gotten some good answers but I want to repeat a couple:

I always start solving battery, charging, electrical or starting problems by
cleaning the battery and other affected terminals. For typical car
batteries which have large terminals on the battery and large connetions on
the cables, I'd advise you to get a little terminal tool at the auto parts
store (it has a two part brush - one part made for cleaning the terminals on
the battery, the other part for cleaning the inside of the cable
connections).

Boat batteries USUALLY have stainless steel screw threaded posts on the
batteries and smaller round connectors on the cables. The posts don't often
(ever?) need cleaning, but the cable connectors do need to be looked after.
You can easily clean them with a toothbrush-sized copper or brass wire brush
and/or sand paper. Regardless of car or boat, the idea is just to keep the
battery posts and cable connections bright metal. This also applies to all
electrical connections, but in my experience, the very first and most common
place for corrosion to affect starting is right at the battery - and it is
very easy and quick to cure and/or prevent.

I'd almost bet this will solve your problem.

Second issue, testing the battery: a boat/marine battery -whether it's deep
cycle or starting type - is essentially the same as a car battery. They're
just built a little different. Therefore anyplace that can test car
batteries can test a marine battery. A load test is the best thing to do if
it's an older battery that you're not totally sure of.

Finally, there are easy "temporary" and "permanent" ways to monitor your
alternator. You might want to have a volt meter permanently installed on
the dash board if you don't have one already. It's a pretty basic gauge as
you've found out. It will show you if the battery has a charge (if the
motor's not running) or if the alternator's working (if the motor's
running). As a temporary measure you can use a simple, cheap indicator tool
as someone else pointed out, or you can buy an cheap or expensive version of
a multi meter at any hardware store or Radio Shack. A very handy tool to
learn how to use, and pretty easy to do so.

Even if you're not enthusiastic about being a mechanic (like me - meaning
I'm a very reluctant mechanic since I have a very large learning curve and
often mess things up the first time), it's very handy to learn to do some of
these things because (1) you can waste a LOT of time waiting for a mechanic
to "get to it" and (2) a lot of times problems happen out on the water than
can be pretty easily solved if you have some rudimentary knowledge and
tools.

It sounds to me like you've demonstrated pretty good problem solving skills
(jumping it to raise the prop) I know it sounds strange, but some people
wouldn't have figured that out and would have just dragged the thing out of
the water and risked damaging it.

Hey good luck and enjoy that boat. It sounds like it will be a beauty and a
lot of fun.

Cam