This is a known problem and I have sent information to Frederick Townes via email, twitter and w3edge website but it still has not been resolved. I have come to the same conclusion that you either have to stick with php 5.3 or enable debug for page cache with php 5.4 on GoDaddy shared hosting. The error I get in the apache logs is "End of script output before headers: index.php"
https://twitter.com/Photonics_Jobs/status/563776880403546112