The first question is: When you say "cheap RG 59, do you mean copper-braid cable, or is it just inexpensive foil+braid RG 59? If it is either, it needs to be replaced. Copper-braid cable is, at best, only 95% shielded, which means 5% or more unshielded. But that's the expensive copper-braid cable. The most common is 65-85% braid, which is15-35% unshielded (holes). All of those holes get found by broadcast TV and radio signals. On the VHF locals, you get ghosting, upper teens through lower 20s, you get crosshatch and other noise in the pictures. Channels 95-97 have loads of garbage (FM radio), and if there are broadcast UHF channels, cable channels ~65 and up will have problems. If the cable has foil, but it is not bonded, there is the potential for the same problems, but to a lesser degree. An amplifier will not help the situation.
If the cable has foil that is bonded to the dielectric, it is probably alright. Make sure that the connectors are real connectors and not the twist-on or push-on type. Preferably, the connectors are compression, but hex-crimp are also acceptable.
The EDA-2100 amp is an excellent amp. Your cable modem, however, should be on its own, dedicated splitter prior to the TV distribution system (including amplifier).