So was it an in-place upgrade or a new installation? It's important to know if the instance-level settings were retained or reset to defaults.

Either way it could be instance level settings like MAXDOP. Is it configured correctly for the new server?

Does the server have the same IP? Sometimes they get moved to another subnet a few hops away introducing additional latency.

The other thing that hits time and again is disk configuration. Yeah it's a brand new server but were the disks formatted to 64kb NTFS blocks? Are the data/log files on separate spindles? What about the underlying RAID configuration?

What are the wait stats for the server? Have you been running sp_WhoIsActive now and again to see what's holding things up? Or possibly even turn on the built-in Management Data Warehouse to start gathering query-level stats, so at least you have somewhere to start.