The following error message from the error log might help diagnose the problem, which seems to be a memory problem. Again, it doesn't explain why one Moodle site with one domain works and the same type of Moodle site in the same directory and with the same settings with another domain doesn't, but it's a start, and i am now fiddling with PHP memory settings to see if I can get anywhere:
[Fri Dec 21 04:07:36 2012] [warn] [client 198.186.192.44] mod_fcgid: stderr: PHP Fatal error: Allowed memory size of 262144 bytes exhausted (tried to allocate 523800 bytes) in Unknown on line 0
[Fri Dec 21 04:07:36 2012] [error] [client 198.186.192.44] Premature end of script headers: index.php
[Fri Dec 21 08:32:55 2012] [warn] [client 84.99.115.129] mod_fcgid: stderr: PHP Fatal error: Allowed memory size of 262144 bytes exhausted (tried to allocate 523800 bytes) in Unknown on line 0
[Fri Dec 21 08:32:55 2012] [error] [client 84.99.115.129] Premature end of script headers: index.php
[Fri Dec 21 09:04:33 2012] [warn] [client 84.99.115.129] mod_fcgid: stderr: PHP Fatal error: Allowed memory size of 262144 bytes exhausted (tried to allocate 523800 bytes) in Unknown on line 0
[Fri Dec 21 09:04:33 2012] [error] [client 84.99.115.129] Premature end of script headers: index.php