Welcome to LQ!
dpkg is a core part of Debian, it is the "apt-get" backend, if you removed it, you will have hard time saving your installation. Better start from scratch again. If you don't want, you can boot in rescue mode or using a live cd and install dpkg by hand again by unpacking the .deb with tar and copying files by hand. DPKG come by default, so I am not sure why you say "Then I decided to install dpkg;". The DVDs also have all the packages, you don't need to download anything else if your /etc/apt/sources.list had correct configuration to use the DVD repository.
If it is your first Linux, you should start with something a little bit higher level, like Ubuntu (quite "experiments proof") or OpenSUSE (a little more fragile) and work your way down. Debian is very good, but it is easy to "try" something and destroy the whole thing. It is even easier with Fedora, Arch and Gentoo. But "too" easy with Debian for new users. Debian is for people who know what they are doing and punish those who don't. I know that very well, I started with Debian and I destroyed my first ~15 installs trying "things"* back in the days. A good part of this is that you learn a lot in the process, but today, there is much better way to do this than 10 years ago (damn, I am getting old...).
*(like XFree86 to early cvs version of Xorg without knowing apt-get existed. Yes, by downloading every packages with wget and compiling them one after the other until it worked, only to find out that my graphic card was not yet supported) <-- off topic anecdotes
**No flame saying that "distro A" is more fragile than "distro B", this is my opinion, not a flame bait. As long as "rpm --force" exist, peoples will use it.