What raw data can I possibly acquire from an 8" Classical Dobsonian Telescope, and a DSLR? Could anything eye-opening to amateur astronomers be computed or calculated first-hand with such equipment? I'm sure scientists must've considered this equipment "advanced technology" at some point in history not too far back...Could I rediscover or calculate some Laws (like Kepler's laws) or some other things amateur astronomers would be amazed to calculate themselves (like the distance to a planet) using this equipment?
An 8" telescope was state of the art in 1686 (even though a modern amateur instrument is certainly much better than Huygens' lenses were) and a normal DSLR sensor has only slightly better properties than plates that were used in astronomy up to the 1980s, so there isn't much gain there, in terms of instrument performance, over fairly old equipment... it's just MUCH more convenient to use. You can, however,re-live old discoveries with it, if you like and you could also discover new things with relative modest instruments. That, however, may quickly become a full-time job, irrespective of what instrument you use.
If you want to understand what Copernicus and Kepler did, it's probably best to read their books, first. They may give you an idea of just how much intellectual and observational effort it took to amass the knowledge that we are teaching in high school, today.
The real problem in observational astronomy is that a lot of what astronomers do is not just linked to the performance of their instruments, but to the total amount of time that is needed to perform high quality research. If you look at some of the finest amateur astronomy imagery, you will find that the "amateur" has spent months or years waiting for near optimum conditions (alternatively you can move to Hawaii and camp out on the volcano... just like the professionals), took dozens if not hundreds of frames and then spent days stacking and processing them with the same tools that the professionals are using.
How about comet hunting? Does it sound like fun to be out there every night that seeing permits to get the necessary observation time for a one in a hundred (or is it thousand?) chance for a first discovery? To me it sounds like that the "amateur" label is not a good one for many of these folks. Plenty of them are just as driven as professionals, they merely never got a job title called "astronomer", but I am sure they would do great work in a professional environment just as well.
Yes, you can do all of that with an 8" telescope... or with a 12" with a cooled astronomy CCD that will be your next purchase (who needs a new car, right?). But would you? Would you spend a couple years measuring the positions of Mars and Venus at least once a week to prove that Kepler was right, after all? We know that Kepler was right. We also know how long it took him to get the calculations done without a computer. Would you use your computer to calculate the orbital data or would you do it by hand, to be historically "more accurate"?
As for the distance to planets... that, I am afraid, is not going to happen in your lifetime, again. The next Venus transit will be in 2117, you just missed the opportunity of two lifetimes back in 2012...
And then there is the aspect that many professional astronomers actually never lay hand on an instrument themselves. They are part of collaborations of professional engineers and scientists specialized on the art of instrument building and/or they rely on the operators of the large telescopes and the satellites/probes they get access to once or twice a year (or once a lifetime like the folks who just flew by Pluto!) to make the measurements for them, and then they sit in their offices crunching the data for a year or two, eventually publishing their papers. The most ubiquitous substance you will find in any science office is paper. Some folks have stacks of scientific publications of colleagues all around them and all they do all day long is to read them. That, like it or not, is what many of the world's best scientists are doing: they collect clues in other people's work. A lot of that (and the raw data) is now on the internet. Nothing stops you from looking at it until you discover something that nobody else has seen, so far. It's definitely out there. And when you do, all you have to do is to write a science paper, submit it, get it peer reviewed and maybe you will even be published. The rest is rinse and repeat.
Or you can do what I do... I grab my \$12 binoculars, I go out on the porch and I look at the Pleiades, the Orion Nebula or Andromeda, the Moon, Venus and Jupiter. Occasionally I lug my \$20 kiddy telescope out there to see Jupiter's moons or Saturn's rings (barely). That is fun, in my books. Driving fifty miles just to get out of the light pollution that surrounds me... that wouldn't be.
In addition to CuriousOne's fine answer, I'll point out that Dobsonians, while easy and cheap to build, are rather difficult to combine with a tracking mount. For really good photos (or faint objects), you'll be much happier with a slightly more expensive 'scope with an equatorial mount and a USB interface to your PC.
In general, don't bother with an adaptive optics add-on (not cheap) unless you're going for greater than 8-inch or so primary.
In any case, even with a Dobsonian, people often discover emerging comets or interesting star clusters. The photography part will lead you to select a camera with extremely low noise (or cooled, as CO said). Consumer-grade cameras probably won't cut it.
I just stumbled upon your question. If you go to astrobin.com and put Dobsonian in the search field. You'll see a huge number of excellent images taken with Dobsonian telescopes. Most are of the moon and planets but a few are of the brighter deep sky objects such as the Great Orion Nebula. There are better instruments to use for astrophotgaphy but if you have access to a Dobsonian and an iphone, you may be surprised what you can get just holding it to the eyepiece! It will help if you check out your local astronomy club. They will be happy to teach you and some even lend out equipment.