My shurflo water pump was accidentally left running when the water tank was empty. It is making a noise but no water is being pumped through. Have I ruined the pump?

It sounds like some water may have gotten into the machine's pump system when you left the cap open. The noise you're hearing during the washing cycle may be due to air bubbles or debris in the pump.
Here are some steps you can take to try to fix the issue:

1. Unplug the machine: Before attempting any repairs, make sure the machine is unplugged from the power source to avoid any electrical hazards.
2. Check the pump filter: Many washing machines have a pump filter located at the front of the machine. Check your machine's manual to locate the filter and clean it out. The filter may be clogged with debris, causing the pump to work harder than usual.
3. Run a cleaning cycle: Some washing machines have a cleaning cycle that can help remove any debris or buildup in the machine. Check your machine's manual to see if it has this feature and run the cycle.
4. Call a professional: If none of the above steps work, it may be best to call a professional repair service to inspect the machine. They can diagnose the issue and recommend the best course of action to fix it.

Remember, it's always important to follow the manufacturer's instructions and safety guidelines when attempting any repairs on your washing machine.

Difficult to work out how you are using and wiring this? The pump is under the sink but you have 30 feet of wire going outside? My guess is that the filter is causing too much back pressure and cutting it off. Then pressure is vented off through the filter and it starts up again. Are you using this with a pond? Not an application for this pump I don't think.
https://www.northerntool.com/shop/tools/product_200647933_200647933

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Try bleeding all the air out of the system or the new pump might be faulty.

If the pump is primed, water will come out of the tank when the pump is running. It make take a little time for the tank to fill, but you should hear the pump making some noise. An un-primed pump just makes a motor noise, not very loud.

The pump should not refuse to pump just because it was momentarily run dry. We do not have that model here in NZ so I'm not familiar with it. Is there a way to apply some air pressure (lungs) to the top of the tank and operate it, or maybe you can find some plastic tubing (2 feet of garden hose maybe) that fits the tank socket, full the hose with water and pressurise the top of the hose while operating the pump. If that doesn't work you are doomed to have to open it up and look inside.

I can't find your particular model pump but, in the picture shown, if thats yours, it looks like two pumps in one. Anyway, I'm pretty familiar with Shurflo pumps and they are diaphram pumps and, the antifreeze may have taken out the diaphams. I'd like to see a bigger picture of it.
http://www.shurflo.com/files/Education-Center/Product%20Data%20Sheets/Fresh%20Water%20Pumps/pds-Extreme%20SS%205.7%2012v%205901-0201%2011.pdf
The pump head should look something like this. I'd replace the diaphram assy.

Take the aerator off the faucet and see if that makes it work better if yes clean the filter in the aerator on the kitchen faucet.

Hello;
Water water everywhere.... The pump you installed has no way of knowing when to stop. Shurflo also has a pump with a pressure switch that senses pressure drop to turn on and back pressure to stop. I'm sure the dealer that sold you the one you now have will have the proper modell for your application.. Good luck and be sure to put a filter in the line coming from the fresh water tank. You should be all set with this recommendation._Ned_

There is a filter screen on the pickup tube in the tank (or there should be) if there is a lot of debris in the tank it will slowly start to plug up the screen and reduce the liquid intake for the pump. If that is not the case then take the spray nasals off and clear the debris from them. Hope this helps you.

If this is a booster pump, many booster pumps like Shurflo have an adjustment at the top (allen screw) to back off on the pump pressure, turn to left to back off on pressure. If it never shuts off this can be an indication of a bad membrane, capillary tube, flow restrictor or automatic shutoff, causing all the water to run to drain. If you have low quantities of water, but pump always runs, this could part of the problem. Also high TDS (total dissolved solids) will cause the pump to work more. The higher the TDS 500+ppm the harder it is to produce quality water. With high TDS it's almost like taking muddy water, running it through filters and getting drinkable water. So the RO and pump have to work much harder to produce any quantity and quality of water.
RJ