I experienced this bug myself several months ago. From my testing, K1 Party Leveler (the file "p_bastilla002.utc" that it contains, to be exact) was the mod that was causing that black screen bug. I reported the bug to the mod author who promised to look into it. This was the text of my bug report:
When I got to the Dodonna cutscene before Star Forge, I was greeted by an infamous "Cutstart Bug". The cutscene with Carth informing Vandar and Dodonna didn't start, there was just a black screen with a cursor. If I used keyboard shortcuts for Force Powers, I was spawned on Ebon Hawk with a hostile Carth and a friendly Dark Side Bastila on it. The bug only affected the Light Side Dodonna cutscene, if I sided with Bastila on the roof of the Rakatan temple, I could play without any issues.
At first I thought that one of my other mods might be interfering with yours (my KOTOR 1 build is heavily modded), so I decided to test K1 Party Leveler on a clean install, with just the Community Patch and widescreen fixes. The bug still occured there. After some testing, I isolated its cause: it's the file p_bastilla002.utc. When I delete it from the Override folder, the cutscene plays, and if I put it back, it doesn't.