Having spent 4 years using my S3iS on a nearly daily basis, earlier this year I switched to a DSLR (Canon 50D) after going through much the same process as you're going through now. Though I have by no means mastered my DSLR, I've used it enough to know that there's still a place in my life for my S3iS - it really depends on the situation and what I intend doing with the pictures.
Buying a DSLR in some ways means that you have to relearn your approach to photography. You mention that you couldn't believe the limited focus range on your friend's camera, and that's a great example of a difference between a P&S and a DSLR - the 35mm-equivalent focal length range of the S5iS is 36-432mm but you won't get a DSLR lens that will cover that. I have quite a common pair of lenses (17-55mm (=27-88mm when you take the 1.6 crop factor into account) and 70-200mm (=112-320mm with the crop factor taken into account)), which gives me a little extra on the short end but is still some way off on the long end, when compared with the S5iS. You'd need a third lens to mimic the (excellent) Supermacro facility on the S5iS.
What will probably horrify you even more is that the DSLR lenses that give the best results are so-called prime lenses, which have a fixed focal length, i.e. there is no zoom capability whatsoever. The reason for this is that a zoom lens actually contains many pieces of glass - there are 16 "elements" in my 70-200mm, for example. The more elements, the more scope for reflections etc off the various glass surfaces, which will compromise the final image quality. So the simplest lenses will give the best results, and a simple lens means a prime lens.
In practice, having a smaller zoom range than you get with a P&S (or having no zoom at all) means you have to learn to move your feet in order to get the shot you want. You also need to get used to changing over lenses on your camera body, though a general walkaround lens (such as the 17-55mm) can help limit that. A DSLR will seem like hard work compared to a P&S!
Another difference is that, on your P&S, what you see on the LCD before you take the shot is generally pretty similar to what the picture will look like. On most DSLRs, you have to use the viewfinder and what you see through that is essentially what your eye sees - it is NOT what the camera will take. Thus if you have the aperture/speed/ISO/etc set up incorrectly, the scene might look fine through the viewfinder but the picture itself will be rubbish - you will only notice this when you review the picture after taking it. Obviously you can shoot in Auto mode so that the camera makes all the parameter decisions, but my point is that you can't rely on the LCD in the same way that you can on a P&S. Some DSLRs have functionality (e.g. LiveView on Canons) that enables you to see what the camera will take (i.e. similar to on a P&S) but it's a big battery drain.
So why does it make sense to have a camera body and three lenses, weighing a couple of kilos, to (not quite) cover the focal range of your lightweight P&S? The answer of course is that, when used properly, you can get much better results out of your DSLR than you get out of your P&S. As mentioned in the previous posts, DSLRs can help address the P&S weaknesses of poor high ISO performance, shutter lag, low dynamic range, etc, not to mention lens issues such as chromatic aberration, fringing, distortion, etc. This is possible because DSLRs have larger, better sensors, and the lenses are not only better made but are generally not trying to be jack-of-all-trades lenses. The trade-off is in size, weight, convenience, and cost (!)
I would advise going with Canon or Nikon. Together, they account for about 75% of global DSLR sales. Though that in itself isn't a reason to buy them, it does mean that if you need advice then there will be more people familiar with your camera body and lenses than if you choose, say, Pentax or Sony or one of the other brands. Similarly, there is a more mature second hand market for Canon and Nikon products. As to the differences between Canon and Nikon cameras/lenses, you could spend the next 10 years reading forums about which is "best", but it's probably a better use of your time to simply go to a camera shop and play around with some of the models. For models in the same price bracket, you are unlikely to find enormous technical differences so your decision may well come down simply to ergonomics.
Most DSLR manufacturers try to make their lenses compatible with all their bodies - both their current and historical ranges. This means that when you're deciding what to spend your money on, you should always skew more towards the lenses than the body. A rubbish lens won't give you a good picture on even the most expensive of bodies, but a decent lens will give good results on a cheap body. As you progress further in photography, you can then upgrade your body but still retain your old lenses.
My experience has been that there are many situations when I simply can't be bothered lugging my DSLR around with me, which is why my P&S still gets plenty of outings. The vast majority of my photos aren't used for anything other than showing friends/family what I've been up to, so the improved quality that I can get with my DSLR isn't critical. The best photos require being in the right place at the right time, as well as framing the shot correctly, so frankly the equipment you have is secondary, but a DSLR will give you a significant technical edge over a P&S. I've found that getting used to my DSLR has meant I've learned a heck of a lot more about optics and lens physics, which is all useful background too. Don't expect to make the change to a DSLR without encountering some frustration along the way, but if you can push through that then you should get some better pictures at the end.
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