I was an ASIC CAD/EDA software support guy in my past life, and a designer now. You wouldn't have the quarter-million dollars for a custom ASIC, but you could do a custom FPGA that would have an ARM CPU, Ethernet, IDE controller, display controller, serial UART, etc., all built into a single chip. Most of these things have open-source hardware descriptions at:

http://www.opencores.org/

Plus, an FPGA would allow you to design *anything* you wanted into the hardware. You wouldn't be limited to assembling off-the-shelf parts.

Just a thought.

- Chris