Let's be clear on this - Are you looking for a "PC" (implying, Intel x86-compatible), or a single-board computer, processor=don't care as long as there is a Linux port? The link you posted is to an ARM-based SBC.
If that's what you're looking for, you might want to look at Bitsy and related products, and similar devices such as the Cerfboard
If power consumption is your major issue, then RISC solutions are really the only way to proceed. However you do need to define your requirements a little more strictly; "133MHz" processor can cover a wide range of performance depending on the architecture of the processor and the board into which it's integrated. Some idea of the target application would help narrow this down.
If you need an Intel-compatible (PC-compatible) board, then perhaps you can look at solutions based on Geode (200~333MHz), or ST's STPC series (wide speed range from ~50MHz upwards). There are also a few boards based on the SiS 550 embedded x86 SoC (200MHz). For these products, look at vendors like Advantech
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and BCM
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Support is much better from Advantech, prices are [generally] slightly better from BCM.
These are all much greedier than your 1W requirement, though - more like 9-10W minimum for a complete system. The Via Epia series of motherboards, recommended by another poster, are *way* outside your power budget; the slowest of them requires about 4A on the 3.3V rail,
1.25A on the 5V rail, and 300mA on the 12V rail, with peak current requirements being considerably greater than that. They don't publish useful numbers, because they intend you to run the board off a standard PC power supply, so those values are actual measurements I've taken when trying to work out a power budget for the Epias.
You might look (on ebay) for a used IBM Thinkpad. I'm not a Linux guy. But, I recall in the 133Mhz days the Thinkpads were the laptop of choice for runnng Linux so Linux shouldn't have much problem with the hardware. Even with a real mouse and keyboard, this setup should consume less than 15W. You might look for two identical systems, so you have spare parts on hand.
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