I just bought a BDP-S3700 and had exactly the same problem.  I could connect to my wifi but failed to connect to the internet.  I called my ISP butthey said as everything else connected to my wifi, it must be an issue with the DVD player.

I found the answer in the Support community, the link is 

https://us.en.kb.sony.com/app/answers/detail/a_id/35254/session/L2F2LzEvdGltZS8xNDgwMjc5MjA3L3NpZC9Y...

You need to enter some settings manually to connect.  The important one is tis

• IP address or IPv4 address - which needs to be set higher than it is on your own computer.

I have an iMac and it is in system preferences, network.

I'm no ID guru but I did it.  I nearley tore all my hair out and was just about to give up and return the DVD player to the store.

Good luck.