Help With Pump Drain

Hi guys. I have a quick question I hope you can give me some advice on. I have a small pit in my basement with a sump pump in it for drainage. When I moved in I connected my pump with 1 1/4 inch discharge to it which connects to my sewer system and used it for a few years.
Last fall I noticed that the pit wasn't draining even though the pump was running. Now I ran the hose out the window so that the basement wouldn't flood. I never got around to fix the original problem until now.
I'll explain as best I can, but basically there is a 2 inch black PVC pipe that comes from the main house drain. then an elbow and is reduced to a check valve and then the connection for my sump pump hose. I'm pretty sure that the check valve has seized causing my initial problem.
I just want to know if I can just get a new 2 inch elbow, reduce it to an 1 1/2 inch, put a new check valve and the reduce again to 1 1/4 inch. My plan was to put all that together, then saw off just before the old elbow and put my new one on. I have tried to just take off the check valve but I guess the previous owner glued everything so it's all together well.
I'm not the best at all this so I appreciate your help and suggestions.
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One question, 1 1/4 seems small for a sump , output goes up greatly with larger pipe if your sump takes it.
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Most areas also don't like sumps draining into the sanitary sewers. Your better option would be to drain out thru the basement wall and away from the foundation. Sometimes this can be done thru a downspout drain but use caution doing this - if that drain gets blocked down stream from the sump, you could end up with roof water back-flowing into your sump and basement.

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look at a water-powered sump pump in addition to the new electrically operated pump for your sump. this will give you dependability for the basement and its potential water damage from flooding and water heater breakdown. and a new check valve as recommended by a plumber who is familiar with your neighborhood construction and sewage and flooding concerns.
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