How hard is it to generate about 10 - 20 watts renewably?

In the UK these days even in Northern Scotland you can see quite an few weather Stations with solar generators on top of top. Short knowing too much about these I would state they're of siamese output to what you privation - the solar panels are about 1-2 square feet.

Another thing to consider is the voltage - you can easily generate at low voltage and most computers can be made to run on 12 volts. You can increase efficiency by removing as much voltage conversion as you can. 12 volts also has the advantage that you can store surplus electricity in a car like battery which are relatively cheap these days.