Basic Web Technology - PHP/ Ruby on Rails or ASP.Net is not that difficult to learn. It may be a good idea to know the basics.
I am not a pure techie and am building a web app. It took more than a couple of months to find the right techie. In the mean time, I outsourced development on ODesk so that there is some momentum by the time I build my own tech team. Now we are almost at the verge of launching our first app.
It is certainly do-able. Takes a little longer and costs a little more. But in any startup, the cost of building the first iteration of the product is not the most significant.
But you absolutely must have clarity on what your product is and who is going to use it.
"Aren't you worried that it takes few weeks(days?) of coding for dropbox team and one update for your solution to become obsolete?"
Wouldnt this logic apply to every project? What if Google Docs just builds a dropbox type app on top of it? Google certainly had more resources and superb tech talent.
I think all companies have their focus and are already very busy getting their product right. If you think there is a need for which you have the right solution - build it.
Who knows - Dropbox might just buy you out.