righty, just sorted out my log in so i can comment on this.
is your tv system complex? are you splitting out to any devices other than what you have mentioned?
what you said about digital either getting there is partly rubbish, yes it is a digital signal, but, at the speed at which 1080X data travels, the wiring is used moreso as a waveguide as opposed to a traditional wire in the terms of what we're used to.
so, down this hdmi cable goes the signal for audio, video, clock sync, handshaking protocol, 5v and some other bits i cant remember right now, think of it this way, if you have a cat5e cable and don't obey the guidlines for the twisted pair and you want to run full duplex gigabit you wont reach that speed. the same applies to hdmi.
as an example, today we went out to a job where occasionally the screen had a purple hue, why? cheapy hdmi cable. £100 lighter and now all is good (ok, its a 10m cable) another job, the image had artifacts and other apparant signal degredation issues 'sparklies' (as they're known) for the same reason, we buy a 'monster' branded cable at £100 or so and it cures the issues the customer has put up with.
Yes, you can use a low-cost cable, but we find we have problems with them, not all the time, but occasionally.
apologies for bad english, its late and i'm tapping on here instead of sleeping.
I'm not saying you shouldnt use cheap cables (people do and they work) just giving a little insight as to why good cables cost more – because they are made to a tighter tolerance, which will be of greater importance when hdmi version 1.4 is rolled out / ratified / whatever.
apologies if my tone is a little curt, really tired but plenty of work to do 😉
jt