Oh the woe I have for the PS2. It's an epic tale of tragedy! Sadly I don't have any deal method to play PS2 games - And I've certainly tried too! I simply haven't found a good method to play PS2 games on my HDTV yet.
I have a backwards compatible PS3 but it sounds like a jet engine when I use it so I have to use a 5M cable and keep it in another room - It's not very accessible though and something I get out for special occasions.
I tried the POUND PS2 HDMI cable... it was awful and looked no better. I've also tried using cheat discs to expand the resolution and had very mixed results.
My current best way to access PS2 games is this...
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Don't get me wrong it's cute! But as a way to experience Triple-A PS2 productions it's hardly Ideal. You can put in some Earphones to the monitor to make it more immersive so it's not bad. But much like the BC PS3 it's not something I have out at all times and is in storage.
Some games are backwards compatible on the XBOX 360 - Crash Twinsanity, Burnout 3 Takedown, the Shenmue II port it sitll my ideal way to play the game! But I don't have many really.
At this point I'm not morally opposed to Emulation, if the games aren't accessible on modern setups and Emulation offers a better way to do so, then I am al for it. My PC is nothing fancy, I bought it online as a refurbished model for £100. However, I've learnt recently it can play a PSP Emulator flawessly which was a nice surprise! Sadly I don't think it is strong enough for PS2 Emulation (I've yet to try it to be fair)