A few thoughts:
1) There are two parts of the protein folding problem: a) predicting the correct final 3D structure of a protein from its amino acid sequence, and b) figuring out the mechanism by which an unfolded polypeptide chain coming off of the ribosome folds into its final 3D structure. I will refer to these problems as the structure prediction problem and the folding mechanism problem.
2) Obviously the folding mechanism problem is more complex and solving this would automatically solve the structure prediction problem. FoldIt is designed primarily to investigate the structure prediction problem. Efforts such as the Folding@Home project are geared more towards the folding mechanism problem.
3) The structure prediction problem is essentially a global optimization problem: given a long polypeptide chain, find the lowest energy conformation of that chain. Searching for the lowest energy conformation is difficult because the search space is large and contains many local minima.
4) The state-of-the-art structure prediction programs are able to generate a decent starting model for the protein structure by comparing the amino acid sequence with the sequences of proteins of known structure. The programs then play around with the structure (rotating bond angles, moving various pieces of the protein around). The program will compare the energy of the structure prior to the change with the energy after and if the change has lowered the energy of the structure, it will accept the change.
5) Often, the search gets caught in a local minima, where small changes to the structure all raise the energy, even though the overall structure is not correct. Often, visually inspecting these "trapped" structures can reveal more drastic changes to the structure that may move the structure out of the local minima and closer to the correct structure. It is this part of the algorithm, recognition of local minima and identification of the large changes to allow escape of these minima, that benefit most from human intervention.
6) With regard to the original question (why isn't biological engineering used more in fuel production), Hartmut Michel, who won the Nobel Prize for his work studying photosynthesis, has an interesting editorial in Angewandte Chemie
(a major chemistry journal) titled, "The Nonsense of Biofuels." In it, he argues that electric cars run from solar energy makes much more sense than using biofuels because of the inherent inefficiency of biological photosynthesis:
His article is a bit too dismissive of some biofuel technologies and doesn't really address some of the issues with solar power, but he does make some very good points. Although biologists often marvel at how well nature is able to perform some tasks, it is good to sometimes admit when we have built devices that surpass nature's abilities.