You want to access your LAN when you are away from home?
What do you want to access?
If you can't forward ports on your router you're not going to be able to use any VPN type method to connect, unless the router supports VPN access.
You might be able to use TeamViewer to access a computer on your home LAN remotely. TeamViewer is free for personal use. TeamViewer would allow you to control a remote machine without too much trouble.
You have to remember that anything you are pulling from your LAN over the Internet will be limited by your upload speed. Normally the upload speed is a fraction of what your download speed is. For example, I have 75MB down and 5MB up. Downloading a movie file, for example, might take a few minutes, but uploading it would take an hour.