The ISP should be able to see the signal levels. It dropping to a slower speed sometime means the router/modem is having issues communicating at a higher docsis level. Hard to say the details of what docsis levels are supported on what networks vary a great deal both between ISP and even within the same ISP in the same city because of different equipment being used. There should be messages in the log if it is having issue and dropping to lower encoding.
It can be a issue with the coax wires, you can see if it works better connected as close as possible to where the cable comes in. Although not likely simple to accomplish there likely is a coax splice on the side of the house where it comes in. You could disconnect the cable going into the house and hook a short coax cable to the modem. Be careful to put this back correctly these connectors are waterproof but need to be tight.
It could I guess also be the modem/router...which leads to your next issue. First I will assume the box you have connected to the coax is both a router and a modem? Most times it has wifi if it is also a router. If it is just a modem issues with network can cause strange ping problems.
Do you have another device you can test with, will make it simpler to determine if you should look at the end pc or the router/network/isp.
General failure most times is some issue with the cables or the pc. It could be the router if that is actually failing but not real likely. Most the solutions you will find if you search are written by people that have no clue. They talk about DNS but even the examples they show are using numeric IP addresses so DNS is not involved. This makes most their other suggestion suspect.
So I would first see if there is a newer driver for the ethernet port. Some of the 2.5g port have a history of buggy drivers and microsoft also load generic ones with their update sometimes. Try to get the driver directly from the chipset vendor website.
It could be DHCP but it is not likely. What you can do is put a static IP on the machine. A quick and dirty way to do this is do IPCONFIG /all. Then go into the IPv4 setting and put those values in. Not the best way since the router might give the same IP to another device but it will do for testing. Change it back to DHCP after you are done or assign a IP address that it outside the range of the normal router DHCP pool if you want to leave it static.