"Database is slow" is similar to saying "the internet's broken" when you cant connect to wifi. There are many many potential causes. We need to do is narrow it down the statements to "this specific query is now running x times slower, or something like that.
you have given one exampe with your backup now taking 30 hours. Now we have a reproducable issue we can test and debug against. Next step is to find out why this is slow.
In SQL Server your first port of call for performance issues should always be the wait stats.
Paul Randall has a great article that comes with a query to look at your wait stats.
I would run this, store the results.
Kick off your backup thats taking 1000% more time than usual.
Intermittently run the wait stats script and store results to a table.
Do a delta to check what wait stats are causing you the most pain when this backup is running.
This may not give you the actual cause but at the very least it will point you in the right direction to investigate the issue further.
I use this process for absolutely all performance issues on SQL Server as a frist step for debugging and analysis.
If your still having trouble after you get the wait stats, post them here.