Sql Server on Windows Server 2008:
Overnight, fullbackups taking 7-10 hours instead of 1-3
transaction logs taking 4-5 minutes instead of 1 minute
Query optimization taking 3x longer
I'm feeling like a disk in my Raid Array (raid5) is faulty or the raid controller or network card, Rackspace is telling me everything is fine.
Any ideas on what/how I need to check?
It sounds a lot like your Write Cache on your RAID controller might have got itself disabled. This is common if your Battery Backup Unit (BBU) has failed. Most cards will switch off write caching for safety reasons in this situation.
Use the Windows performance monitor and take a look at the disk queue length metric for your volume. If things are high, you can consider that there is a disk issue.
Other things to consider: has your dataset changed significantly? Are you running other processes on the system that you weren't before (anti-virus)?
You mentioned that you think that this might be a network card issue - why? Are you backing up over the network? If so, try backing up to the local disk and see if it takes a significant amount of time.