Your last two lines of the error log show that it was up and running for about 3 hours before it caught a signal to terminate itself..
PHP Warning: Unknown(): Unable to load dynamic library '/usr/lib/php4/pgsql.so' - libpq.so.3: cannot open shared object file: No such file or directory in Unknown on line 0
Thats most likely the issue. Postgresql isn't being built for php4.
Do you need Postgresql? if you don't you could just disable the option.
I may be wrong, but i think you need to do a mysql-clieent install first.
I found this on another forum:
yum install mysql-develhttp://www.linuxforums.org/forum/servers/59648-mysql-server-problem.html
yum install mysql-server
yum install php-mysql
yum install mysql-client
yum install mysql-debug
yum install mysql-bench
I don't think they mean for you to install all of them? but yea. Try to do a mysql-client first and then try the regular mysql or just a mysql-server
Do you have cpanel at all? If you have cpanel and can access whm you can use easy apache (also via command line with /scripts/easyapache I believe) to do this very easily and it will get all dependencies it needs.