Would a lack of grounding increase noise problems in phono circuits?

I have had problems with noisy phono circuits ever since I moved into my house. There is a radio tower like half a mile away, that I can see clearly from my windows, and it comes over my phono stage, and my guitar amp.

I also have no grounding anywhere in my home. The outlets have a third prong, but testers read "open ground". I rent, so there is not much I can do (it is a standalone home though, no shared wiring). I often have noise/hum problems in concert with my radio pickup problems.

If I had properly grounded outlets, would that solve or improve my RF and noise issues? Or are these things all unrelated, and I just got lucky?
 
Safety grounding is not going to help much with RF interference. There is too much inductance in any amount of wire, like the power cord. A quick fix might be clamp on ferrites on your cables next to the amp(s). A likely fix to the phono amp is a series resistor about 1K to 4k7 on the inputs, and 10K to 100K for the guitar amp. Some may suggest paralleling capacitors, but this rarely helps because the cables are about 50 or 75 Ohms, which is what matters, not the amp impedance. Note that ferrite cores come in different densities for different frequency ranges. Lower radio frequencies need more inductance, but hi-mu core losses make them ineffective at higher (FM/TV) frequencies.
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The third prong MUST be earth-ground or else be unsafe, besides not meeting the National electrical code. The code enforcement guys in the town where you live may respond to this.
Split clamp-on ferrite cores has very mild effect, better to solder in a multi turn ferrite inductor in series with the input signal(s) and even the power supply. Shielded IEC945 power cord are cheap on Amazon.
Better equipment typically have EMI filtered AC input modules, but external ones can work too. Tone arm better be grounded, as it may be the only shield the cartridge wires have.
The frequency of the interference is of interest as all ferrite chokes have a frequency response cure that should be suitable for the problem.
 
Yes, safety ground is important and the lack of one is dangerous and will cause hum problems. But it will not help much with RF problems. If there is any plumbing handy, or a ground rod, you could add a ground connection to your power bar etc. I have seen attempts to solve this problem by connecting neutral to ground that went wrong because one outlet was wired backwards, connecting hot to ground, and damaging equipment that was connected together between two outlets. We have not seen this in Canada/USA for ~50 years, but I understand that electrical standards in other parts of the world are not enforced. The OP must choose to deal with it the best he can or move.
 
An electrician could install a ~8 foot ground rod and tie it to the water pipes, AC mains ground etc, if it is missing.
Not a simple affair. It has to be done according to electrical codes, and if the building is not in compliance it should be condemned, as it would be unsafe. Talk nice to the landlord, or seek legal advice.
 
I grounded my power strip to a water pipe. It made the ground tester happy. But, it didn’t fix my problem. I will note the hum changes in level if I move the equipment around. My preamp has an external power supply connected via an umbilical cord. I can move the cord around like an antenna to “tune” the level of noise.
 
The very nice Hagtech .pdf covers most of the stuff to trouble-shoot a sensitive/low signal input.

There are many types of "noise", which generally can be considered any unwanted signal.
AC hum, Thermal Noise, RF-interference, feed back, ground loops, etc etc.
When trouble shooting start at the power supply, if dirty nothing helps. Old dried up electrolytic caps?

AC hum can be induced magnetically, by conduction, or electrostatically, shielding works for the latter, but magnetic shielding is hard to deal with, here distance is the lowest cost remedy. Interconnects can be quasi-differential, by using microphone type wire with a twisted pair inside a shield, where the pair is used for the signal and the shield is connected to the "ground" only at the connector at one end, which then typically is connected at the start of the signal path.

Divide and conquer, check by reducing the variables. Using a "Non Contact Voltmeter" may be helpful identifying electrostatic fields. There are many things that can go wrong, assumptions can be off by a mile.

Check leakage currents with a DMM in AC voltage mode. I would not want more than a few volts AC between DC power supplies and AC mains ground. Input resistance of DMM; 10 meg / measured voltage is the leakage current.
 
Short the input of the amp, if noise persists, there is an internal amp problem, unrelated to ground.
VHF tuner tubes like the 6DJ8 etc can respond to very high frequencies. Also consider bad or missing solder joints, failed thin film resistors, loose connections, bad tube sockets, failed tubes. Resistors have a voltage limit, I have replaced a few from over-voltage wear out, with wire-wound types, which do not suffer the same issues as thin film types.
Larger, a bit more expensive than film, but much cleaner. The Vishay Dale RS00547K00FE73 could work as a plate load.