Problem is SOLVED.
Main cause of this issue was too small memory_limit for PHP. It was set to 32MB and PDF generation module (which is loaded in calendar only when there is any event in view) was exceeding this limit. Script was dying without any information and output.
Memory limit can be changed in several places and it depends on server configuration. During runtime PDF generation module was trying to set this limit higher, but it was too late and it was crashing. Swapping two lines of code fixed this certain issue and calendar worked as expected on Raindj server.
During solving this problem, we've discovered several other issues and fixed them, but one of them is still present and it won't be fixed. More information here.
Thanks Raindj for cooperation and giving me access to your server.
Regards,
Adam