It may not be quite what you're thinking of, but there are a number of very inexpensive "PC-on-a-stick" designs that have an HDMI output; we're talking $25 (Raspberry Pi, although it's not a stick - lol) to $80. Most are Linux or Android based. Many of them also have network connectivity, whether ethernet, wifi, or bluetooth. Just google "stick computer hdmi wifi" for an overwhelming number of 'em for wifi alone. Many will handle 10-bit 1080p fine, with the appropriate software. For example, on the Android stick PCs, you can simply run "MX Player" (free or paid, the free version has small banners at the bottom of menus) to play just about anything with few issues. If I can play unconverted 10-bit 1080p on my Evo 3D, which also requires rescaling, with no perceptible problems, it ought to work on a wide variety of devices.
Remember to do some research on any model(s) you are interested in, to make sure it can handle the load of 10-bit 1080p. I'm not sure, for instance, that a Raspberry Pi could handle it. I'm not sure it WON'T, but due diligence is in order.
Alternatively, if you already have one, you could simply hook up nearly any relatively recently-manufactured laptop (within the past 3 or 4 years) to your TV and use it as an HTPC, especially if it already has an HDMI- or DVI-out; most models with a discrete graphics adapter will have one. VGA-out will usually work, depending on your TV, but isn't often the best option, and won't preserve "HDCP" status for protected content. Remember, you'll need to pipe audio separately for DVI (and VGA), as it has no audio, but this generally is easy to take care of with an 1.8" stereo-to-dual-RCA adapter (available for $5-10). This is the method I use, and is a great use for a secondary laptop that isn't otherwised used often.
If you use any kind of surround-sound system, you're going to want to go with HDMI, as it preserves all the audio data. Otherwise, you're pretty much stuck with stereo.
