You indicated that the cables connected to your modem/router may be showing signs of damage or wear and tear. Damaged or old cables can cause problems such as poor speeds and dropouts.
Try replacing any damaged or very old cables as these may impact the performance of your service. Refer to the website for your modem/router manufacturer or speak to your preferred internet provider about the right type of replacement cable to use for your device.
If your telephone wall socket is showing signs of damage or corrosion, you may need to have a registered cabler attend to repair it.