The slide lock (slide release) does not hold the action closed after the hammer falls. It is simply there to keep everything locked up until you pull the trigger. It has nothing to do with the action opening up upon shooting.

Take the gun apart and look at the top of the bolt. You will see a chunk of steel inside the bolt and a piece of it sticking up through the top. This piece is the locking block (part #73). This is what keeps the action locked up until you pump the gun. The steel that actually sticks up through the top of the bolt is what is the actual locking surface and is what is actually keeping the gun locked up until you cycle the action.

The Bolt slide (part #74 - or the part that the bolt sits and slides on when you take it apart) has a surface on it that pushes up the locking block into its engagement surface (square hole cut into the barrel extension).

Your problem is that the locking block is not locking into it's engagement surface. This could be caused by a number of things.
#1. check the top rear corner of the locking block and make sure that it is not burred over. #2. check the rear corner of the locking engagement surface on the barrel extension and make sure that it is not burred over. If either of these are burred over stone down the burr and see if it will lock up as burrs could prevent the locking block from fully engaging the locking surface. #3. There is a pin that holds the locking block inside the bolt. Make sure that it is not broken or bent in any way or has walked out of one side. If it is then replace it or push it back in. #4. Look at the bolt slide and make sure that the angled bit of material is not broken or excessively worn down. If it is then take it to a gunsmith. #5. Look at the bottom side of the locking block. The forward most flat surface should not be worn down excessively. If it is then take it to a gunsmith. #6. Make sure that the barrel extension is not cracked or broken behind the locking surface (square hole). If it is then replace the barrel.

If it's not any of these then I don't know what to tell you with out looking at it.