What about port TinyLinux on this 24Euro ARM computer (50pieces for 19Euro)?
newbielink:https://www.olimex.com/Products/OLinuXino/iMX233/iMX233-OLinuXino-MICRO/open-source-hardware
[nonactive]Super small, cheap, SDCard, TVout, audio pins, USB... Made in Bulgaria

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iMX233 ARM926J processor at 454Mhz
64 MB RAM
SD-card connector for booting the Linux image
TV PAL/NTSC video output
1 USB High Speed Host
Three buttons
2x30 pin GPIO for connection of other hardware
PCB dimensions: 3.00'' x 1.70'' (76.2mm x 43.2mm)
Nominal dimensions: 3.40'' x 1.70'' (86.4mm x 43.2mm)