I've recently started exercising/working out again after a long period
of doing nothing much but sitting around.  I've discovered that the
first workout of any muscle group after such a long period results in
stiffness, soreness, and lack of extension for several days after the
fact, but once I've cleared that barrier, my muscles are open and
receptive to future workouts with nothing but the usual pleasantly
sore warmth the next day.

Anyways, three days ago I went running on a treadmill (walked for .1
miles, ran until I couldn't run anymore, slowed to a walk till I
caught my breath again, ran some more, etc) for about 35 minutes.  The
day after that, I lifted weights, focusing on my arms and shoulders. 
Yesterday, since I was pretty sore, I took a day off.  Today, my arms
are still pretty sore and I can't fully extend them, but I'd like to
go running again.  However, I've read somewhere that doing
cardiovascular exercise while your body is still recovering from a
prior workout can prevent the muscle growth you were attempting to
achieve in the first place.  Is it safe to run today?  If not, how
will I know when it is?  Will it be when I no longer feel any pain in
my arms at all?  I don't want to waste too much time.

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Request for Question Clarification by keystroke-ga on 18 Aug 2006 06:54 PDT

From the sound of things you have pulled your muscles, did you stretch
before the exercise? Always stretch before exercise otherwise you can
seize up badly like you have noticed now. When your arms are
extendable once again you should be ok to carry on training, however
it seems like you are over exerting yourself and you don't have the
ability that you used to have when you last went to the gym.

Start slower and lighter than you used to do it at and work up
otherwise you will do yourself more harm than good.

--Keystroke-ga

I think that if you want to make exercise a habit, it should be
enjoyable, and it isn't good to do it when you are in pain.

What you're describing is commonly called delayed onset muscle
soreness.  As you noted, it's most pronounced when you're getting
started/restarted with an exercise routine.  You can help prevent it
by doing the following:
- stretch after you work out.  Slow, steady stetching of the muscle
groups you just worked out seems to help quite a bit.
- drink plenty of water (dehydration will make your muscles more sore)
and try to take in an adequate amount of protein and carbs after your
workout, preferrably within 20-30 minutes.  These nutrients are
required for muscle repair, and some limited evidence suggests that
the muscles are more efficient at taking nutrients up from the blood
immediately post-exercise.  Anecdotaly, I can often tell a difference.
- take a day off if you're really sore, which you already did.

Running with sore arms will only inhibit muscle growth because your
burning calories.  If you keep your nutrition and hydration adequate,
I don't think it will have a noticeable impact on muscle growth.  So
if you're otherwise motivated to run or work out, I'd say do it.

Good luck.