Constant problems with internet. The other connections - phone and tv seem to be pretty good

I have had problems with internet for about 6 to 8 months.  I have an airport extreme as the router for several years and recently changed to SB6141 Modem but I still seem to have the same problem.  I had a service technician here several months ago and he advised my cable was old and probably the problem.  I reran the cable in the attic with rg6 but ran into same problem.  I initially had it split so I could watch tv in the same room but I assumed that was causing the internet to drop so I ran another separate cable for the tv alone but still problems with intermittent disconnections.  I usually have to reboot both the modem and the router in order to re-establish a connection.  I have 5 televisions (small one outdoor under the patio and another small one in the kitchen)) throughout the house with 6 available hook up connections.  The one available unused hookup connection has a booster connected to it (installed by Cox).  I also have but one computer, router, and modem hooked up to the cable internet with several wi-fi connections for laptops and tablets and printers.  I am unable to get the lower channels on one tv.  I am assuming that I may have too many connections for the four way splitter in the attic (also installed by Cox).  Before I go through another frustrating attempt at diagnosing the problems can anyone offer some suggestions as to what procedures and in what order should I try to figure out what is wrong with my hookup or to determine if it is just a bad connection.  I also have an 8 way splitter but have not tried to install it yet..