Just a follow-up....
After trying everything (using IO::Socket::SSL, using different actions, double-checking MD5, etc...), I got so desperate that I have generated a new private key, and bingo! It works!
Could anyone at Tucows confirm that it is indeed possible that one _has_to_ generate a new key in order to use the HTTPS interface? (I haven't changed our key since... well, since about 2001 :-))
Ahhh, I am so happy now :-) Will have my own package without any BEGIN blocks or global variables, and with Class::DBI and Template soon :-)))
Regards, - Csongor