I have been reading the forum for a while, and think I understand most of these issues on their own, but would like to ask a question about a couple problems.
I just bought my first "real road bike" (a Scott CR1 Pro). It is a 61 cm frame, and I really love it. However, I have a question about "dialing in" the fit. I notice that when I ride even a short distance (4 mi or so) I get some tingling in my hands while I'm riding on the hoods. I think I can flatten my back out more or ride in the drops to relieve some of the pressure, but then my boys start to tingle.
Are these issues that I can make some hardware adjustments to correct or do I need to "suck it up" for a while until I get stronger, and maintain a more flat back?

Numb hands can be one of the most maddening issues to try to solve, in part because there are so many causes. For some folks, they are just prone to carpal tunnel-like symptoms and can suffer from it even with their fit dialed in.

Otherwise, it could be resolved by better padding (quality gloves, quality bar tape), OR less weight on hands (how much saddle to bar drop?) OR technique (gripping bars too tight, not changing hand positions periodically) OR poor core body strength, meaning your hands are taking the brunt of all of your front end weight.

Now I'm kind of worried... I'd never noticed before, but the saddle to bar drop is only about one half inch. Does this mean I'm too stretched out?

Very common to be fit to your bike with your arms out too far. Easy to put your hands in distress that way. Simple fact is if your hands get numb while putting pressure on them in a cycling position then you have to be readjusted to have less pressure on your hands. Anything else is simply a band-aid solution. The bars may need to come up or in, it really depends on how you were originally set up on the bike. Another way to get the weight to lessen on the bars is to reposition your saddle back. You really should find an expert who can look at you on the bike to determine the correct course of action. If your current level of shape does not allow for you to get positioned on the bike in a course that gets the weight off your hands then you may need to seek out a band aid approach till you get yourself in better shape to ride the bike without any undue comfort.

I wanted to post and thank all of you for your words of experience and wisdom.

I went back into the bike shop today. I first rode the bike 16+ miles to the shop to make sure I could clearly describe all of the problems I was having.

A little back story is appropriate here. The CR1 pro is an 06 model, and was DEEPLY discounted because it was the only one left and they wanted rid of it.

Frankly, I could afford this bike, but could not afford even the 07 comparatively.

As I mentioned in my OP the numbness could be relieved by bending the arms and kind of rotating the pelvis forward a smidge. However, this caused numbness in my nether region. So, I got out a level and found that the stinking seat was drastically tipped nose up. Essentially I was riding with my butt clear back on the seat and my pelvis cocked back to keep from smashing the boys. This caused my elbows to lock, and shot all the vibration up my arms. I didn't have the tools to make the adjustment (I got them today though) so I took it in. We flattened the seat out, and I rode it low and fast all the way home no problem (except a little fatigue).

I do have a pretty short stem on there (80cm), so, to be completely honest it probably is a bit big anyway, but it was the best bike I could afford and I love how it rides.

Thanks so much to all of you!