(This isnt a solution more like a helpline)
The Problem seems to be serverside... maybe the rented server doesnt support mods, or if so maybe a vital mod like forge isnt installed properly, try reinstalling the server from scratch then try to incorporate the old server bit by bit and that should pinpoint any problems, also to your problem of converting classic to lite, try using a map editor to copy vital chunks (buildings, factorys... etc) and replace old mods parts (condensors... etc) with a random block (dirt,gravel...) , dont use the entirety of the map because then some materials wont generate causing problems for the players.
Also, Check out this guide to help you convert...
http://forums.technicpack.net/threads/how-to-convert-tekkit-classic-world-to-tekkit-lite.34915/