I had problems with no audio when I first tried connecting my Mac Mini (early 2011 revision) to the TV via HDMI, but they resolved themselves after an OS update went through. The Mini with an HDMI socket is definitely capable of sending audio over HDMI, but I don't know if laptops outputting via mini-displayport are.
The first thing to check, though, since I didn't notice it mentioned here - you do have to go into System Preferences, open up the 'Audio' option and on the second tab (if I recall correctly) where you choose your audio output, select the row that says "TV - HDMI" or something to that effect. We have a Panasonic, and it reads "Panasonic TV - HDMI". Before you select that item, all audio will be routed to internal speakers, headphone jack, whatever your default output is. If audio output isn't supported, then you just won't see an entry for your TV in that list. (This was the problem I had when I first tried; it didn't think it was supported over HDMI, and there wasn't an entry for my TV in the outputs list.)
(Also be aware that once you select the TV output, OSX will disable the volume control, so you'll have to do all volume adjustments with the TV remote.)
As to a mini-displayport-to-DVI cable then a DVI-VGA cable, here's one potential answer as to why it didn't work: DVI cables can optionally carry two signals; a digital one and an analogue one. The cable and the socket are designed to be backwards-compatible and capable of carrying an analogue signal, but that doesn't mean that everything that outputs via a DVI socket will necessarily be sending both the digital and also the analogue VGA signal.
All a DVI-VGA adaptor does is connect up the relevant wires in the DVI socket that carry the analogue signal to the relevant wires on the VGA socket, so if your mini-displayport only outputs a digital signal (I wouldn't be surprised), then the analogue pins on the DVI socket won't be carrying any signal and that would be why you don't get a picture when you connect it up to a VGA input socket.
(I've only ever hooked my Mac up to a TV using a DVI-to-HDMI cable on my older Mini (which had a DVI output which definitely included the analogue signal) and a straight HDMI connection on the newer Mini.)