Have your startup get you a separate computer. Not mixing work and personal life extends to not doing work development on your personal machine or vice versa.
While they're at it, add in an apartment so that your work computer is not kept at a private residence...
It sounds like this was a summer internship, having to lug a separate computer around because Dropbox doesn't support separate accounts seems like a huge work around. The whole point of Dropbox is that the files are wherever you need them.
It's really the only solution if you want to maintain some degree of personal privacy, and don't want to incur all your employer's liability on your personal account (and vice versa).
It sounds like this was a summer internship, having to lug a separate computer around because Dropbox doesn't support separate accounts seems like a huge work around. The whole point of Dropbox is that the files are wherever you need them.