Diane, without circulation and water movement you are creating a breeding haven for mosquitoes [think West Nile, Encephalitis, Malaria Etc,].

My opinion is that the pond should be drained, cleaned out and the repairs to the stone work done as needed. That way you know what you have to deal with and you are starting with a clean pond.
A filter system installed outside of the pond before you re-fill it with new water would be more than beneficial. Proper filtration keeps the water healthy for the fish etc, by removing the waste products produced by the fish and decomposing plant matter.

There are out of pond filters that can be homemade and do a great job of conditioning the water.

If you decide that is what you opt to do, you may have to treat the new water with a de-chlorinator, if you use city water. With well water it isn't necessary to treat it for chlorine content.
It may seem a daunting task to a "novice", but there are lots of good people here who will be glad to help you through it.

Knowing the dimensions of your pond [length,width, depth] and what type [ brand and GPH output] of pumps you have there, plus the type of existing filtration, would help the members here, assist you in reclaiming the pond.
"Horton"

Hi Dianne,
There are a few of us from the great white north on here, and from colder zones, Alberta. Mosquitos are the main problem as Horton said, filtraton is also important. enjoy your pond

You don't "have" to have circulation in your pond. But it sure helps it to be nice and with circulation and filtration you can have more fish and clearer water.
It depends on what you want for your pond.
I have always had a filter/pump for my ponds because I think it is better for the fish, ect.
I have a neighbor that has a very small pond and when she had goldfish she had real issues with the neighborhood kids coming to the pond and catching them. So she took out the pump which allowed it to sort of go murky, put in only minnows so she could still have some fish but they wouldn't be real demanding and get large AND the kids wouldn't be able to see them easily nor catch them. The kids lost interest in her pond and went away. In a couple of years she put her pump back in and added goldies again. The kids were no wiser and it didn't hurt her minnows. Goldfish do not demand a filter nor a pump as long as you have the pond carefully stocked to a LIGHT level and if you don't mind it being somewhat murky, then it is fine. The fish will eat the mosquito larve mostly. The plants will provide some oxygen for the fish and if you havn't had a problem yet, you are unlikely to except in the HOT part of the summer. Then you might have some distress with your fish if you have to many. Personally, I would try to fix the problem and run the pump/filter if you have one.

Good luck

I agree, you can have a still pond but with certain conditions. How many fish and plants do you have or want to keep? What type of pond do you enjoy looking at? Some like the natural look while others like their ponds to be crystal clear. The pond is never really still anyway because you will always have some sort of wind movement which adds a BIT of aeration. Be careful to not overstock or overfeed fish in a pond without filtering and do keep your plants to a 1/2 surface area coverage. Be warned! You will have to do all the hard work and maintenance on a pond that would normally be done by a filtering system. You have to keep your plants pruned of dying foliage/flowers and keep as much muck as possible off the bottom of the pond of any dying or decaying matter. The fish will take care of the mosquito's, as will dragonflies and frogs, but use a mosquito dunk if you prefer. It's tedious and back breaking work. The good news is...the choice is yours!

Botanical gardens (pick one out of the many greats!) are a great source of information regarding still water ponds.

Nance

I have about a dozen ponds including container ponds and only one has a pump and filter.

I use mosquito dunks in all that don't have fish.

None of my ponds has stagnant water. They are all clear and healthy and full of frogs, dragonflies and other aquatic critters and plants.

IF you have soil on the bottom of your pond and fish, they will root in it and stir it up so your pond won't be crystal clear but that is fine for the fish.

Since your pond is doing just fine right now, I would not worry about adding the pump again unless you have a low oxygen problem later this summer. You can tell by going out to the pond very early in the morning, if you see the fish gasping for air at the surface of the pond you need aeration right away. This would be all the fish gasping not one or two it is very dramatic and unmistakable.