In investigating the other rooms, Percy will not have any issue getting inside. However, Vex will not be able to get inside and Percy will not be able to bring anything out of the rooms. They will need to work the doors open if they wish to take anything out, and it will take about a day for each door. (Just to keep in mind of IC-timeline reasons.)

The room of most note will be what looks like a storage room (space closet) with a few boxes of what seems to be materials used to fix up the ship itself. There is a material that can be used to fill in holes in the wall, a kind of fast acting and extra-strong tape, etc. You seem to have found a repairs closet.