Regarding your Samsung dvd player with hdmi. Read and follow the instructions in the owners manual.
My honest opinion, at least what I would do in this situation, would be to return the Bose system and get a receiver that has hdmi connections for your dvd player. I would then, if money allows, buy a set of bookshelf speakers for the front channels, a center channel speaker, 2 surround speakers and a subwoofer. There is no need for the HK amp, imo, at this time. You have not spoken about what your HT needs are so it is difficult to be more specific...do you need to have small satellite speakers for room decor purposes or are larger speakers fine?...what do you want from your HT system? movies, music, gaming etc. Are their room limitations? etc.
A receiver with hdmi is around $1000 though you may be able to get one for less...search around.
The speaker system may cost another $1000 depending on what you want. So basically for 2K or a bit more you will have a great sounding system...much better than the Bose...and the ability to run your dvd player through the receiver to the tv.
Your Philips direct tv should also be able to connect to your receiver via component video cables providing a great picture.
Check out the Paradigm line of speakers...they are Canadian and, imo, sound great...they also have several lines from modest cost to "whoa how much?" levels. I have the Titans which cost $220 US and the Atoms costing $200 US and love them.
Good luck and keep us informed.