Noise , sounds like ungrounded, all the cables are fine , the connection is grounded

Several possibilities (i have experienced all):

1. 120V.AC line noise. Try moving to a new receptacle in a different room or breaker. Try a In line AC filter (like a Furman power filter/conditioner)
2. RF interference. Plug in a different core and guitar to isolate.
3. Guitar wiring. Bad ground internally or pot (volume) became ungrounded.
4. Defective amp preamp section. Pot or transistor.

A bad ground connection?. Try tightening the nut on the phono plug first. You can pull out that section where the cable hooks into and visually check the solder connections.

Looks like you need a new jack or you have a loose ground. That is why it works when you touch it - because you are grounding it. Check solder connections before you plug it in, and ungrounded instrument is potentially dangerous while using an amplifier

How new is the amp?

A single faulty solder can do that...I'd try returning in to the seller.
Have you tried a different amp with the same equipment?

Sounds like a wiring issue.

Hope I've helped
PvT

First thing: Make sure ALL and I do mean ALL of your interconnected equipment is POWERED from the SAME receptacle. Powering different parts from different receptacles in a building will surely get ground bounce buzz and ALSO subject the equipment to hazards of circuit damage.
The audio connecting cables should be BALANCED lines where possible... either XLR or TRS cables. Problems like you are having are common when CONSUMER grade equipment is mixed with PROFESSIONAL equipment. Anyway, get all the stuff powered from the same receptacle and get back to me if you still have the problem. Note you may have to run three wire extension cords if devices are separated a bit... the pro's have to do that to avoid noise. All devices should have three wire (grounding) cords and/or grounding wires connecting chassis...

1000 Watts? Well, those are peak values. !000 watts RMS into a 12 inch speaker and it would smoke... this is some of our inflated advertising. But that is beside rhe point... now on to your problem: What you are having is a ground loop. You may have to do more than one thing to correct this here is the things to do in the order to do them to solve the problem:

1. Connect the piano and the speaker to the SAME power source or receptacle, even if you have to run an extension cord, three wire of course. Plug all of this ONLY into a grounded outlet, if your house has only two wire plugs, then you need to get an electrician to install a grounded receptacle.

2. Use Balanced lines. This means XLR or TRS balanced cables between the piano and the speaker. Use the 1/4 inch jacks output, not the RCA ones.

3. Since the AUX outputs do not support balanced lines, the next step require you use DI box. They are about $20 from Guitar Center and others. With very short 1/4 inch mono cable connect the piano to the DI box from the L/R mono piano to the high impedance input port of the DI and set the ground lift switch to "LIFT". Use an XLR to XLR cable from the DI box to the speaker. This last step if needed is the last thing in our bag of tricks to break the ground loop that can cause the buzz. Dirty power, if you have lamp dimmers can be a source of the noise.

Iis ALL your equipment powered from the same receptacle? It had better be... ground bounce can destroy input circuits in these units. I don't have the schematic but a common problem where XLR connectors go into a mixer is they have radio-frequency noise suppression caps to ground from each side of the XLR input. These caps are often lower voltage rating and can be popped by ground bounce or ungrounded equipment being connected before the ground connection is made. When one goes, there is loss of half the voltage or 6 Db of power gain. Since these RCA's are right at the XLR they MAY connect and have these caps and one may have shorted. That means the repair shop I am afraid unless you are adept at electronics. Most of these mixers are a pain to work on that area as all the knobs and screws have to come out/off to get the circuit board away from the panel to work on... I wish I had the service manual to give you more info...

PLEASE in the future power all equipment from the same receptacle or power source AND for units that don't have three wire power cord, NEVER change cables that can break the ground connection such as the RCA cables while power is on to any of the equipment. This will save repair bills...

This is from your friendly electrical engineer that works with this stuff and repairs his own...

LIKELY this is a TYPICAL poor connection at the jack. It is not uncommon to have slight noise IF the plug moves as you shake it.

AS A test, restrain the plug so it can't move.

Another source is a FAILING instrument cable. Get ones with GOLD plated ends as they are less prone to oxidation.

ONLY open the guitar after you have exonerated the cable. The jacks do wear, but more commponly the cable is at fault. The connections inside are USUALLY solid and NOT a problem.

If you can access the jack, you could increase the spring tension.

First though, see if moving the plug where it plugs in creates noise.

MAKE sure you have it connected to a three wire circuit that has the ground. A lot of these style amps will buzz if they are left ungrounded.

Also search for sources of buzzing light light dimmers.

Further, power supply electrolytic filter caps are suspect.