The Akasa Euler S is the simplest, most straightforward option for a fanless PC powered by a (35W) desktop CPU. The slim heatsink case does require a Thin mini-ITX motherboard (and it's pretty tight in there) but the building process is a child's game, and just so clean. Order it from performance-pcs, amazon.de, amazon.co.uk, or order a complete PC from our friend Matt over at Fully Silent PCs.
Thin mini-ITX motherboards are rather hard to find, although no less than four of them were announced last week: The GIGABYTE GA-IMB410TN, the ASRock H410TM-ITX, B460TM-ITX, and the ECS H410H6-T12. Could Thin mini-ITX be making a comeback?