There is certainly a market for this abroad, as One Laptop Per Child (OLPC) - and Intel - have demonstrated. The OLPC laptop is, incidentally, based on a stipped down and heavily customised Linux installation.
In the UK, there may well be a market for a similar system to the OLPC one - that is, Linux-based. Indeed, the OLPC system itself may well be suitable for primary school age. Linux is also useful for higher education courses (even when I was in HE 15 years ago we had plenty of Unix machines, and I'm sure these would now be Linux). However, for a school environment, a monitor/keyboard/mouse is not an optional extra.
For a parent wanting to get 'little johnny' a PC, they should be getting them what they use at school. No sense having one system at home and a completely different one at school. Chances are that'll be Windows right now, as that's what the vast majority of schools use, and also what is provided by the various laptop schemes.
For 'average joe consumer', you have a problem. Most of them will have used Windows PCs at work and will when they get a PC for home, they'll want Windows too. OpenOffice is a non-starter as well. I actually tried that with my parents, and though they could use it, they much preferred Works. Works requires Windows, which blows your Linux PC out of the water. These, too, will want a monitor/keyboard/mouse.
There is a market for a headless Linux box. That market is dedicated servers/NAS boxes, but this segment is already covered by numerous companies, both at the low- and high-end. This is also not a big market outside the business sector, and I doubt they'd be interested in £99 PCs with support as an optional extra.
Do some market research (I recognise you're trying here, but given the responses, I'd suggest this forum is definitely not your target audience), draw up a business plan, and if you can justify it, then do it. It's your money after all. If you can prove us all wrong, then by all means come back and tell us.
