Just did some sluthing and it appears your site is in the maintenance mode. Don't run a 2.4 anymore so don't know if this is true or not but in higher versions of Moodle there has been a change to behavior in maintenance mode. If set via Moodle UI, no one can login - not even admin level user. But one cannot login to reset it.
So add this line to config.php:
$CFG->maintenance_enabled=0;
Turns off. To turn it back on, change the 0 to a 1. No need to restart/reboot ... just access with browser.
In your config.php file do you have a line for the admin directory? The default to it is:
$CFG->admin = 'admin';
Do you have an 'admin' directory in the moodle code folder? Has it been renamed xxx_admin? Make the admin config line match the folder name. On your old server there might have been some directory (admin) used for account administration. On new server, that may/may not be in affect.
As far as the error_log ... a clip of that might be interesting ... remove any IP addresses ... replace with xx.xx.xx.xx and remove any site url with something like mysite.com if you do.
'spirit of sharing', Ken