Well, according to the error log you have a saved tekkit file that is interfering with the startup program
try going back through the computer files and fully deleting any other tekkit files
Title: NEI bug
Version: 1_0_3
OS: Win7
Java Version: 32*
Description of Problem:
-Evolved skeleton spawners do not display in NEI
-NEI will not show any items and will crash if you type in the search bar if it is used on a world created before v1.1.0
Error Messages:
Error Log: