Please use FTB app - the FTB launcher / classic launcher is not supported anymore.
If you still have issues with FTB app, please post new log.
With that said - looking at your log, it looks like you might have a 3rd party Antivirus software or other security software that causes issues for you.
Also with just 4gb of ram on your machine, you will not be able to play any of the newer packs - if you're lucky you might be able to play a few of the 1.7.10 based packs (1.7.10 being the Minecraft version), or earlier packs.
You need to leave some for your OS, so do not allocate more than 3gb with your current setup.
1.7.10 based packs or earlier needs around 2-4gb allocated
1.10 based packs or later spans from 4gb -> 6-8gb, depending on pack and version
Don't run a lot of other programs that might want ram, to free up - reboot and only start the game (checking the current log you only got 1220mb free)