I think your code got severely stripped out. Can you let me know what's happening when you insert the {JFBCLike} tag? Generally, that will be replaced with the <fb:like ...> tag automatically by JFBConnect. Are you not seeing that happen, or is something else occurring.
Some possible suggestions are simply moving the JFBCSystem plugin to a lower ordering (higher number), so it fires later. It may just not be executing at the right time to detect whatever it is you're trying to do.
Other things to check are if you have a Render Key set in the Misc tab of the social area. If so, you'll need to make sure that render key is included in the tag: {JFBCLike key=1234}
Hope that helps,
Alex