fresh installation under CPANEL/Wordpress/Softalicious, admin login just does not work at all

Why don’t you just download the most current copy from SuiteCRM and just install it manually.

It’s not that hard. There’s a great video on youtube about how to install SuiteCRM on shared hosting.

I assure you it works. If it still doesn’t work, you should consider a different host. I have a bunch of installations running on Godaddy shared hosting. You have to tweak some settings in the PHP.ini file (as noted on SuiteCRM installation guide), but it runs fine for me.