I don't remember when the change was made but look to see if your car has a red wire connected to the positive battery post. If it does follow it to the 25 amp fuse holder less than 24" away. These have a tendency to corrode over time and are familiar problems. If you have one clean up the contacts.

There is a white fuel injection relay attached to the firewall above the passenger's feet. Remove the bolster to open that area up. You should feel/hear the internals move when turning the key to the run position. This should coincide with the brief running of the fuel pumps. Sometimes tapping the relay with a screwdriver handle while trying to start the car will engage the relay. If this is successful you can usually resolder the circuit board as the solder joints have a tendency to crack over time.

There is also a procedure to bypass the fuse and relay involving fuses 4 and 6 in the fuse box. It involves using a jumper wire to force run the pumps. It has been awhile and I am not positive but I believe The jumper is used to connect the left side of fuse 4 to the right side of fuse 6. Perhaps someone can verify this.

With the jumper in place the pumps should run and since it ran on starting fluid it should run with the jumper in place. This would indicate a fault with the 25 amp fuse under the hood or the fuel injection relay
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Any twenty minute job is just a broken bolt away from a three day ordeal

You might have the same problem I've been dealing with. If the car was parked with fuel you may have a tank full of varnish, like I did and posted about it quite a bit. When you turned it over it could have pumped that varnished gas all through the system, that's what the previous owner had done to my car before he sold it. Now the car I'm restoring was parked for at least ten years (I think it was closer to 15) with about 3/4 tank of fuel, so I had about the worst scenario with this. It could be your pumps but it could be anything in the fuel system up to the intake manifold--or everything, that was my problem, it all had to be either replaced or deep cleaned from the filler cap to the manifold. If its turning over check to see if it has spark and also open the oil cap to see if the cam is turning, that's a good sign that the engine has compression. Pull the fuel line off the rail, put a mason jar on the line to catch what comes out and turn the engine over, and see if anything comes out, that will tell you if your pump has any life left in it. See what the fuel looks and smells like, if its dark and smells like varnish that could be your problem. Next thing I might do is to check the injectors, mine were completely crusted and it was easier to replace them than try to clean them. A varnished fuel system is a nasty, time consuming and potentially expensive thing to clean, I really hope you don't have to deal with that.

This is not going to be easy to answer from this side of the keyboard without some more information.

Can you describe what the AAA person did to determine that the fuel pumps are at fault?
Did he/she check if there is a spark?
Can you hear the pumps run for one or two seconds when you switch on the ignition?
Did you add the new fuel before or after the first attempt?
What is the condition of the fuses and fuseholders?

Spray some starter fluid into the intake. If it starts then suspect the fuel pump. Gasoline can get nasty when old.