Most console RPGs are found on the PS or PS2, or if you go back further, the (S)NES and some Sega systems. Also, most RPGs are turn-based. At least the traditional ones in the style of the Final Fantasy series.
I'm not sure why you despise turn-based RPGs so much. I typically see it as a trade-off. Turn-based RPGs generally have more involved stories. "Action RPGs" generally take focus from the story and shift it to the gameplay. Both are great in their own way.
These are the ones I've played.
Playstation:
FF7, 8, 9
Wild ARMs
Lunar: SSS and EB
Xenogears
FF Tactics (this one is SUPER turn-based, as it is a "strategy RPG," which essentially is a complex synthesis of normal turn-based RPGs and chess, but it's great fun and a good challenge)
If you don't care about graphics, the older FFs have also been re-released. All of these should be fairly cheap, with the possible exception of the Lunar series which may be too rare to be cheap. My favorites of these are... well, all but FF8.
;
PS2:
FFX
A good game, to be sure.
On the action side, you can't go wrong with Zelda, though from what I've seen of friends playing the N64/GC ones, I may actually prefer my GameBoy copy I was given by a friend (Link's Awakening).
Eh, that's all I can say. Good luck.
