Before using a hosting site you need to record. And this seems to be the main problem.

I really doubt that you can record live videos from all your cameras. Even if you can get video from multiple cameras, if I'm not mistaken, high quality video comes only from a single one.

Even if recording from the single camera is enough, there might be a problem with it. It is the software that comes with DVR that should be able to do the recording on a remote computer. DVRs use different protocols and formats so I can't even suggest you any alternative software to record from them.

You can try to record with a streaming video recorder, maybe it will work for you. The only stream recorder I know that can somehow send your recordings to a remote location (using the YouSendIt service) is Replay AV.

Of course you can use screen video capture software on a remote computer. However I don't see any reason to backup your recordings on a remote host after recording with it. You can use a RAID array or whatever other system on a remote computer to store your recordings.