Should I upgrade home theatre to one with HDMI?

You can connect the DirecTV receiver to your AVR via coax or Toslink and get Dolby Digital 5.1 and run the HDMI cable directly to the TV. This is how I hook up my DTV HR-24

$1000 should be enough to buy a decent receiver with xt32 and a new 3d blu ray player.

Simple solution:
HDMI to TV and toslink from the TV to your receiver. Your tv should have digital out.

Imhififan, I see a lot of debate in the forums about being able to use a splitter (even a 3D one) to pass 3D video to a monitor and Hi-def audio to the receiver and everyone seems to be saying that it doesn't work.

Have you actually tried it using a Blu-ray with HDMI 1.4 and a receiver using HDMI 1.3 and got it to work for both 3D video and the advanced audio codecs???

For me the easy solution would be simply to buy the Sony S790 Blu-ray player that has both an HDMI Video output to the TV (for 3D) and an HDMI Audio output to the AVR that will do the advanced Dolby and DTS codecs. But since I have only one Blu-ray disc with 3D video so far it's not that big of a problem.

You do not mention te primary purpose for the HT system. Movies, Music, TV, Gaming or all of the above?

Here are my thoughts. Everyone who mentioned that you are missing out on the new lossless formats, namely Dolby True HD and DTS Master are correct. These audio formats truly sound amazing, some of the best recordings I have heard in over 35 years in this hobby. And I am not talking movies in 5.1 or 7.1 lossless (although they are great) - I am talking about music, particularly Blu-ray concerts that sound simply spectacular. Without HDMI 1.3 or higher into a processor or AVR that can decode it, you are missing out. Optical or digital coax cannot carry these signals. They can only do lossy formats which are the old Dolby Digital and DTS.

Now if all you are concerned about is TV or even movies (Blu-ray or DVD), IMHO the old lossy formats are just fine. TV and DVD can only do the old lossy codecs anyway. If you have a Blu-ray player, you still have the lossy soundtrack that sounds just fine for a movie. So running an optical conmnection between player or cable box and your current 5.1 Denon processor is all you need. But if you want music and want to take advantage of the new lossless formats, get an HDMI equipped processor or AVR. In fact an AVR with PRE-OUTS connected into your 5 channel Denon amp would be the most cost effective solution. Just make sure the AVR has PRE-OUTS. They all have room correction, some proprietary like Pioneer MCACC and some licensed like Audyssey that is found on Denon and Marantz products. They all do a good job. Good luck.