You have to provide exact render settings and comp settings. No sound in H.264 could simply mean an MPEG-specific settings mismatch.
I don't see your comp timeline. Your size is also non standard. Try rendering to a jpeg QuickTime or try using the adobe media encoder and try and work with standard sizes. H.264 is very picky about frame size.
i don't see how frame size or video length would touch this. but since we are talking about it, i didn't touch those values. i recorded the footage on full screen and took the footage directly into AE. and my screen size is standard, don't know how it changed in those settings.
Test render 4 or 5 seconds of your comp using a production codec like Quicktime Jpeg and see if there is audio there.
If there is not audio tell us about any other audio you have in your timeline. Convert any audio that is mp3 to aiff or wav.
show us the timeline so we can see what you are trying to do.
Illegal frame sizes will foul up all kinds of things in the render cue... This has been said by me before and by Mylennium. It's true.
Try using the Adobe Media Encoder and a default render setting.
Tell us about your AE version, OS and other things. Even with all your screenshots your question does not provide enough information to give you a direct answer that will be guaranteed to work.