Your mediafire link does not work.
That log you posted shows that folder /mods in folder /Minecraft server on your desktop is empty.
You have no mods installed in it, not Galacticraft, not NEI, not Damage Indicators.
You need to put the mods in the /mods folder, inside the Minecraft server folder, like I already said.
Still nothing?
I just now looked at screens and I seen 1.7.2 and also 1.7.10 folder....delete that one you dont use. If you removed all BUT GC, did it worked?
well , I can give you latest patched 1.7.10 Cauldron server, it runs well on my server. Just delete all and put the files in server folder. However it is not pure forge, this one can run mods and also plugins (bukkit ones)....just be sure that starter of server runs minecraft_server.jar .
https://www.dropbox.com/s/09mq83lcxzbgrra/update serveru.rar?dl=0
Your latest log is quite strange, mine has 16k+ lines, but none of your first lines.