Unless your amplified 8 way splitters are two-way amplification (passes signals in both direction), they're not suitable to connect your cable equipment to, either your cable modem or your cable box. Your cable modem of course is both sending and receiving data at the same time and if you put it on the output side of a cable distribution amplifier that doesn't pass signals in both directions properly, it's not going to work.
Even amplifiers that are labeled as two-way can be suspect as they aren't going to be two-way at all frequencies or at the frequencies that your particular cable modem or cable box uses for upstream communications. Charter in my neck of the woods always puts a two-way passive splitter on the incoming line as the very first device after the grounding block, and runs a line to the cable modem off one of the two splitter outputs. Then the rest of your equipment goes on the other port through whatever combination of splitters you need. Unless the amplified RF distribution equipment was provided and installed by Charter themselves, they're going to blame it first for all your problems.
And I'm not sure how many local IP addresses a cable modem can provide using DHCP before it chokes (maybe only one), so connecting an ethernet switch to your cable modem without it being a router (a router has the ability to hand out IP addresses, a switch usually not), you could be having IP addressing issues from that configuration. Always better to have the modem connect to the WAN port on a router, have the router set to DHCP mode to deliver whatever number of local IP addresses you need in your system (and your devices set the same to accept a local IP address from the router via DHCP), and use an ethernet switch (or two) on the LAN side of the router to give you the number of ports you need in your system.