We have CentOS and Fedora server running on old hardware. We got new Dell servers.
We are looking any open source tool which can take backups and restore all the partition as it is, with out rebooting the server.
You better get used to things like filesystems, volumes etc.
Please answer the following questions to complete my answers:
answers was: no lvm, ext3 fs
My answer is: your system can be backed up by standard utilities (tar, dd), but do not expect the backup to be easily restorable.
you can save the partition table and mbr by issuing
dd if=/dev/sdX bs=512 count=1 of=/backup/mkb-backup.img
after that, archive your devices with tar,
Next time use LVM (support snapshots, makes backup easier) and a filesystem has dumping utility (xfs_dump for XFS, for example).
The 'without rebooting the server' part makes it impossible.
The main problem you'll have is that ALL hardware is different. You need different drivers with different settings on the new servers. Also migrating a system to different hardware without any preparation mean downtime if you have to retain any state information (i.e. you have some kind of database that is updated).
Given your current status I recommend something like this:
If you had your server running within a Xen or VMware you could have done a live migration. But this would mean you prepared before creating the servers you have now.
While i've never had luck with it myself on ubuntu, mondo/mindi might work for a hot image and restore.