Internal Server Error 500, Godaddy ultimate shared linux hosting, front page redirect

Here is my situation. I have my dev version of the site on godaddy economy shared linux hosting and that works perfectly fine.

My production live site is on godaddy ultimate shared hosting on linux. I have the same code base on both these places. But the production site is throwing internal server error 500 from the past 3 days. I have the login destination and front page modules installed and this 500 error happens only when users login and being redirected to a different landing page.
I set up such that anonymous users go to http://www.mydomain.com/publics and when logged in on this page, they get redirected to http://www.mydomain.com/landing.

This setup works perfectly fine on the dev site, but in production, I am getting the 500 error when the redirect to landing happens. Once this error is thrown, if I just type any other url of the site, I am getting to those pages fine.

The only difference between the dev and production site is the data in the DB. Both the sites were working fine for many months now and this 500 error has been happening since last 3 days only. Obviously, the godaddy tech support is of no help. THey just said they did some apache update on all servers 3 days ago and have been adamant that it has nothing to do with my issue, but the timing of when my issue started is so close to this update.
They are suggesting I move the site to a different server to test. I am a bit nervous about this and don't want to lose any prod data.

I am getting frustrated with this. Anybody else have this issue? PLEASE HELP. This is what I see in the error log

[Fri Sep 30 10:20:26 2011] [error] [client 59.93.86.42] Premature end of script headers: index.php
[Fri Sep 30 10:21:10 2011] [warn] [client 59.93.86.42] mod_fcgid: read data timeout in 40 seconds
[Fri Sep 30 10:21:10 2011] [error] [client 59.93.86.42] Premature end of script headers: index.php
[Fri Sep 30 10:56:53 2011] [error] [client 59.93.86.42] Premature end of script headers: index.php
[Fri Sep 30 11:21:37 2011] [error] [client 59.93.86.42] Script timed out before returning headers: index.php