Before you worry about anything else, you need to get the pool cleaned up and the water balanced. In order to do that you must get the pump and filter working. You must have a filter of some type whether you convert to salt or not. If you don't want a sand filter you can switch to a cartridge filter or a DE filter. Many benefits to doing so, especially true if you do eventually switch it to a saltwater pool. DE or cartridge style filters do a much better job of filtration and do not require back-washing gallons and gallons of water down the drain. All filters require maintenance though. Many people use a sand filter and get along just fine, if you get a lot of stuff in the water a sand filter may struggle to clear the water and require frequent back washing to regenerate the filter.
A saltwater pool is still a chlorine pool. Chlorine is created from the salt water using a chlorine generator by means of electrolysis. The advantage of this system is you won't need to buy and transport gallons of bleach and manually dose each day. If you have been told the benefits of salt is that the water is much better than chlorine and the pool just takes care of itself, then you have been told incorrectly. A salt pool still requires maintenance, testing and requires carefully balancing the water just as any pool does. Some do prefer the feel of salt water, but make no mistake it is still a chlorine pool and requires much of the same testing and balancing, plus it requires adding hundreds of pounds of salt and expensive hardware to produce the chlorine.
Your pump may have an air leak, simply need primed, may have a valve shut, may be clogged with gunk, pool water level too low, very hard to say. The first order of business is get that pump figured out and running. Also, you absolutely must have a test kit, a TF100 or K-2600 is what you need. If you need help the numbers from one of these kits are the only ones we are truly going to trust.
Post some pics of your setup and the folks here can help you get the pump figured out. Add some details about your pool such as gallons, size and equipment to your signature so it can be easily accessed with each post. You need to work on getting as much of the solid gunk out as possible. There are many types of skimmer nets and leaf bags that you can drag across the floor to help pull any solid material up from the bottom, once the pump is working you can use a manual vacuum to pull stuff off the bottom and send it directly to waste. There are other things such as a leaf eater that can connect to a garden hose and suck up leaves and silt from the bottom. The more of this you get rid of the easier it will be for the bleach to clean the pool up to sparkling.
