Backup mySQL database

To get into phpmyadmin to backup existing mySQL database. Relatively small databases. Current phpmyadmin login shows that the following error : #1040 - Too many connections No help is available from service provider. ## Deliverables The databases are for a handicap website. The service provider cannot be contacted but the servers are still up. Currently trying to migrate to another provider. All other files have been backed up but unable to backup mySQL databases as unable to get into myPHPadmin account. Coder will have access to web control panel (HELM). There is no access to SSH. Coder will, if necessary manipulate asp code to close mySQL connections. Coder after getting access into myPHPadmin is to make a backup of all databases inside there.