It looks like you also applied to Harvard. Given that they have the same policy (requiring letters from each PI you've worked with), how did you deal with them? 😛
My guess is if you don't have a letter from a research experience, they'll treat it as a fairly minor experience for you (since you weren't there long enough/didn't make enough of an impact to get a letter), but I doubt they'd toss you just because you didn't have a letter from an old project.
Good luck!