Step one: Get rid of AVG. If you read the stickies you'd know that bloated piece of shit causes problems. Get Microsoft Security Essentials or Avast. Both are great, and will protect your computer better without screwing you over.
Step two: Update java, update video drivers (why not, can't hurt?), delete your tekkit folder (%appdata%), download a new launcher, and reinstall.
If doing all of the above doesn't work, we'll go from there.
If you come back having only done one or two of those things, and then say it still isn't working, I'll leave you to the wolves so to speak.