NAS Drives

I have a Seagate HD Drive that I use as a NAS. It originally came with a Go Flex Home program that was discontinued. I was able to continue to use the drive connected to my Linksys EA9200. All my devices, (TV, Sonos, Computers, Blue-Ray) were able to access the folders on the NAS drive and we could easily drop pictures, music files and backups. All that changed when we got our Comcast xFi. The NAS drive is connected to the xFi via ethernet and I was able to get the Sonos to see the music files and play them. However, nothing else can access the drive. The drive shows on file explorer and has an IP address, but I can't get into it to access the file folders. When I try, it just times out and I get an error. Customer Support has been no help as they do not understand what a NAS drive is and we go round and round. When I try a look up solutions I get into port forwarding and quickly get lost as I'm apparently no longer tech savvy. Seagate has been no help because the drive is legacy and no longer supported and I fearing may be beyond its useful and practical life. 

I'm looking at a Synology two-bay Diskstation, but before forking out $500 plus for the NAS and the two drives, I want to make sure it will connect to the xFi and I'll be able to access the folders. I plan on being able to just move what is on the old drive to the new.

Is this something that I should be able to do on my own? Will it work? Will the xFi router do as intended and what is the best way to set it up?

Any help or suggestions would be greatly appreciated.