For me anything hard to change is hardware, anything easy to change is software. Hence the sensible FSF position on software on ROMs being like hardware and software in EEPROMs being like software.
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A definition that I like comes from Renzo Davoli and is basically that hardware is made of atoms, software is knowledge.
ROMs are made of atoms whose internal organization defines the behavior. And while you can pass to someone a copy of the "source" (or binary) for that ROM, it's not the same as the ROM (the person has to build the ROM based on that code), so I think Renzo's definition very agrees that ROM is hardware.
Of course, under this definition, today in 2016 it is impossible to buy a computer¹ whose software is completely free.
I think the usual A20 boards qualify: they have some ROM holding proprietary code within the SoC, but since that's hardware it's OK, and you can run pure Free Software on it (you may need proprietary software if you want to use MALI, and you may also need proprietary firmware to use surrounding wifi chips, of course).
Stefan