[NeighborsComplaint]

Guys, you can't "fry" an input jack on an amplifier. The only parts that aren;t metal are the insulators (phenolic). Have you never soldered? The blue color on the soldering tabs is the plating's reaction to the heat applied by the soldering gun to attach the leads.
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OP, if you are using a known, good connecting cable plugged into the amp, you will get a loud hum when you hold the other plug end in your hand and touch the tip. You're grounding the circuit and causing the hum. If that isn't happening, then the problem is in the cord or the amp. Just make sure the replacement connecting cable isn't also defective by plugging into a working amp at the music store.

If the cable is good, then the jack (receptacle for the plug) in the amp is suspect #1. It should make firm (snap-in) contact with the cable's plug tip and have 2 wires soldered in place. If that is the case, then the issue is deeper in the amp. If the amp-on light is lit, you have power. If not, the switch or transformer is damaged. If you have power and no sound, in all likelihood, the output transformer is burnt out. The small solid state amps use a switching transformer rather than a permanent magnet type because the former is cheaper and that's just how they roll and they are typically the weakest link.