Win2DS is not mimicing your computer desktop, it's actually remotely controlling it (via VNC). So really, it's just allowing the DS to be an input and output device for a full desktop.
What the OP wants is basically a full desktop OS, in a pocket-able form-factor.
This is not currently possible on the DS, but perhaps you might be interested in the
Open-Pandora (which is only slightly larger, albeit much more expensive).
It's an
extremely powerful (think N64 and DreamCast emulation and the ability to play full HD H.264 videos) handheld computer designed for gaming and for regular desktop use. It has a full alpha-numeric keyboard, a 600 MHz ARM processor (over-clocking to ~900 MHz on average, which is actually safe and is officially supported by both the official OS and the official creators), a powerful 430 MHz DSP core (to help with videos and music and some games), an 800 X 480 widescreen display, dual SDHC slots, two gaming nubs a d-pad and gaming buttons and a
TEN to SEVENTEEN hour battery life under heavy use.
The only downside is that it's being produced by a group of guys who met on the internet, so you have to pay in advance (a preorder) and it's taking a hell of a long time. It is actually being shipped right now (take that, vapourware-twats!) but it is still quite a wait.
Sorry for my gushing, but I'm a Pandora and DS nutter so I always talk about the other in either community.