Please help me. What do I do?

Hi guys

I have a 4 days spring internship coming up next week (UK internships for first year students with a fast-track AC for next summer at the end of it) but one of the afternoon clashes with the final round of an entrepreneurship competition that I signed up for.

I sent HR an email a few days ago with this issue, and asked when would the day approximately wrap up. One of the reps sent me back with simply saying it is expected to finish at 19pm (I would have to leave at 16). Then I sent a follow up email explaining the situation in more detail (5 teams winning 3k in funding and an accelerator programme) and saying that I understand this is unfortunate timing and an inconvenience, but this is a great opportunity to expand my project. And that let me know if this works for them.

One day passed. Then I sent them another email saying I wanted to check in again to see if such an arrangement could be made, and that I would like to keep my options wide at this stage and would really not like to not lose either of these opportunities.

Still didn't get back to me.

Was I unprofessional? What should I have done? Am I right in assuming that I don't want to work for such a company anyway? I am not sure if I should cancel this internship or start taking part from day 1 but still 'try' to leave on Tuesday (there is no way I am skipping the competition so it might get a bit 'intense').

This is for a 2nd tier IB.

Your advice is much appreciated.

Thanks.