If I received an F on a research internship course over the summer, would I be automatically rejected?

I have a BA in economics and political science from UT Austin. Unfortunately on a summer research internship course I dropped the ball by not submitting enough hours into the project. It wasn't because I dislike research, in fact it was interesting although mundane in what I was doing.

I went on a vacation with my dad who passed away three months later, which tanked my grades even lower in my final year

My UGPA is a 3.26 (junior year a 3.58, mainly bc of the econ) and I have okay softs otherwise. I did well in a political internship that had a final research project but it was my own (bad) project rather than a project I was contributing to.

Do I look like I have a chance here? What do y'all think?