in many ways the brain does act as a large database -- rather than storing the same 'objects' over and over and over again, it appears that in many cases the information stored in your long-term memory 'references' other memories.
Annecdotal evidence: I've lived in the US for the past 7 years, but grew up in the Neterlands. I 'remember' much of my childhood with English dialog now, even though I know for a fact that the conversations in question were in Dutch. The brain is a funny thing indeed.
And this:
The strength of these connections is analog, which affects the thresholds at which nuerons will fire
is a very good point as well. Digital machines like todays computers have much lesser capabilities than analog or non-binary digital systems.
The only reason computers use binary (0-1) is that things like tertiary (0-1-2) and up is too difficult to accurately present, since a '0' and a '1' aren't actually absolute values, but constitute a value withing a certain range of signal strength. For tertiary (or above), you either need to have smaller tolerances which require a more accurate power system, or you need to deal with higher voltages and longer switching times between extreme values which either leads to more heat and/or to slower switching.
The brain, in contrast, is a self-modifying, self-repairing, self-replicating, self-programming, and very 'fuzzy' analog machine. All of the above is near impossible to replicate in digital form, and building something fro scratch in analog form would be orders of magnitude more difficult thanks to the lack of discrete rules that binary needs to make sense out of anything.
But even if you can make a technically fully functional 'brain', the really hard part will be to actually turn it on and get self awareness. A brain from a dead body won't really do much for you, even though technically it all seems to be there.