I am trying to connect to my mailbox on my hosting via imap_open() (php) . But its throwing authentication failed error.
According to my hosting provider they have disabled telnet for security reasons. Could disabling telnet cause php to not be able to make an imap connection ??
No. These are different protocols. IMAP is working on port 143 and telnet on port 23. Your confusion likely comes from the fact that IMAP is a text based protocol and you can use the telnet client program to control an IMAP session.
If the error messages states that the authentication failed, this is a strong hint that the IMAP server is working and answering your connection attempts but you somehow failed to offer proper credentials.