This sounds like a very naive view of biological systems. The complexity of the most complex thing computer science has created (I would argue that is the Internet) is still trivially simple compared to the brain.
I am not naive about the difficulty of the problem.
Are we spending enough time looking for those techniques?
We aren't necessarily looking for better techniques all the time. It could simply be streamlining a step or two in order to make medical research loop tighter. It could mean eliminating a process or two that shouldn't be running.
Whatever the case, our researchers should be thinking about novel solutions to the problem instead of mechanically running the lab. The world fastest machine might not be able to make an intractable problem tractable, but it shouldn't be a bottleneck.