Quote: "Sorry if I wasn't clear. I mean graphics that look as good or better than PS3 or Xbox 360, which I guess would be 1080p (as good as) or 2560 x 1440 (better)"
You can set it to any resolution you want. However, the graphics might not be up to par with what you're expecting.
This is for two reasons:
1) Mipmapped textures have a maximum resolution of 1024x512, so you can't have high-res textures.
2) There is no bone animation, so characters' limbs will be all jointed.
DarkBASIC Pro solves both of these problems, but it is harder to learn and the free version has tons of ads.
Speaking of which, you can just download the DarkBASIC 1.2 "upgrade" (you'd have to google it) and you don't have to pay The Game Creators a dime. However, this does not grant you a commercial license to sell your games.
If you want to sell games made with DarkBASIC Classic, you're going to have to cough up $10. It's well worth it.
However, the free version of DarkBASIC Pro does grant you a commercial license, and DarkGDK has a commercial license too, and it's free. However, with DarkGDK you'd have to learn C.
Alternatively, you could just use FreeBASIC, which is as easy as DarkBASIC Pro and completely free, but it lacks almost all of the features. In that case I would recommend using FreeGDK (you'd have to google it).
The only problem with FreeBASIC is that it's not a TGC product, so you wouldn't have the support of the community here. In that case, you could buy PureGDK, which is basically like DarkGDK for another form of BASIC.
However, why buy PureGDK when you could just buy DarkBASIC? Or DarkBASIC Pro? Either one is good.
So yes, high def is possible, but you can't just click-click-bam create a game. If you want that, you can buy The 3D Game Maker, but it costs $99.
Bottom line, either buy DarkBASIC or download DarkBASIC Pro.