According to MySQL's documentation, if you use innodb_force_recovery=1, the server will start even if it detects a corrupt page.
Still, there are a couple of things you may want to check.
Are there any relevant errors in mysql's error log? cat /var/log/mysqld.log
Is the file system OK, can you create files with touch in the same partition ? ex. touch /var/somefile.txt
If you have a full backup of your databases, as you mention in your question, you can delete the ibdata and ib_logfile(s) and recreate them, then restore your databases. This will resolve any corruption issues you may have in the innodb files.
The steps are:
delete the ibdata and ib_logfile files.
rm -f /var/lib/mysql/ibdata1
rm -f /var/lib/mysql/ib_logfile*
Start MySQL (which recreates the innodb files)
Restore the dump
mysql -u root -p < mydump.sql
As long as you only delete the innodb files(ibdata and ib_logfiles), your users and their access rights to the databases will still be in tact.