If you need to use one, use ONE good quality splitter. I recommend asking for a dedicated Line for the modem if possible
I'm still concerned about link between modem and router, should be blue on the light.
possible the modem could be bad maybe. I would test it out on a friends or neighbors house, maybe even a family member if close buy. Take the router too. Last resort.
Lets get the ISP involved and go from there. You might go to best buy for frys and get a different router, something with Gb WAN port and test that blue light. I should be blue.
Need to move any t.v. splitters and amplifiers and test with out them.
Keep us posted on how it goes with ISP.