If you are running Windows 7 Professional, Windows 7 Ultimate, or Windows 7 Enterprise you can connect to them remotely using the RDP protocol, otherwise the simplest way would be to use a version of the VNC client/server, but things like sound and printing would not then be supported. Some less common 'remote' protocols do support sound, but things are then getting complex, or 'commercial' (eg: they are not free).
To get to your RDP or VNC equipped PC remotely you will need your desired client, which, to your spec, would need to include RDP or VNC embedded into the firmware or a 'thin' OS. I daresay there may be some specialist devices out there that have this functionality, and perhaps a low-cost, atom-based laptop or MID (Mobile Internet Device) but I suspect they will be much more expensive than a run-of-the-mill, low-cost laptop running a stripped down (ie: fast booting) version of Linux. An Android-based tablet would probably give you a nice remote 'pad', but possibly not the experience ('all the functionality') you want.
Short answer: There's probably little out there for a sensible price that gives you all you want.