Devices fitted with two-prong plugs often have a signal ground available (e.g., a dedicated ground lug on the rear panel, typically used with turntables, in many cases), which should be utilized and should eliminate hum. If not fitted with such a connection, verify chassis (using an ohmmeter) is electrically tied to low side of input/output connections (i.e., very near 0 Ohms) and connect components together using an external wire or braided cable. If there is more than one (common) path to the power line ground for your audio equipment, you will likely have hum and/or perhaps a potential shock hazard. If your system includes devices that employ both power and signal grounding schemes, you'll need to trace out which is which to eliminate hum and/or shock hazards, if they exist.
The low side of RCA (unbalanced) connections are typically tied to ground (power or signal, depending on construction) internally, with balanced connections having a dedicated ground. These grounds are signal connections and shouldn't need to carry excessive current as mentioned previously.
Also keep in mind that for 120 VAC in the US, the neutral (white) is tied to ground at the electrical panel. Many years ago, my folks purchased a cheap, Western Auto stereo (not double insulated) with a two prong plug. When my brother and I used it, the chassis would 'float' at 120 V, shocking us if we were grounded. If the plug was reversed, operation was normal.
Good Luck!