Right-click on the SH4.exe and choose "Properties" from the context menu. See if in the "Attributes" section on that first "General" tab, if the "Read-only" box is ticked. If it is, clear it, then activate LAA again. I'll try to get the mod running on my machine later, and see if I can get into the Museum. I was almost like 99.9% certain we could enter the museum, but not 100%, of course...
In the meantime, what OS are you using, is it 32-bit or 64-bit, how much RAM do you have in the machine, and where (which folder, or "path") do you have the modded game installed?