GS608 only allows single port connection with new modem

House is set up with modem to GS608v4 then ethernet cables only to various Cat 5 outlets; no wifi router.  This worked well with the old modem but switched that out for new Arris modem from Spectrum (to be compatible with whatever they've updated).  Now, the GS appears to only connect with the first computer that reaches out to it.  Ran thru diagnosing this with Spectrum, and the conclusion is that Spectrum's signal(s) and modem are functioning well but there may be some sort of compatibility issue with the switch when it comes to allowing multiple devices access.  To sum up: yesterday 2 or 3 computers, a printer, and internet TV could operate simultaneously.  Post modem switch, only one computer connects at a time (doesn't matter which port is being used; haven't tried the printer or TV but assume it's the same).  modem and switch have been shut off multiple times, cable ports switched, my laptop (which could not establish connection at the time of troubleshooting with Spectrum because my wife had the single access) was manually pinged (not sure what that really means, but it didn't work)).  I still have the old modem and will switch back tonight until I can get this sorted.    

I'm fine with getting a new/updated switch, but only if I'm pretty sure that'll fix the problem.  Any ideas?  Keep in mind that I'm not really a computer savvy guy (my description above probably shows that...) but can understand the concepts if explained.   Thanks for any ideas.