Dishwasher not filling after replacing sink faucet
Normally it is that the shutoff valve that you closed never reopened.   Really even if it is debris you are probably forced at this point of removing the valve just to troubleshoot.   There is no use disconnecting the dishwasher as this probably isn't the issue and by disconnecting you are causing potentially more issues.   If you have pics I can give you more exacts.

Update:  Based on your current pictures.  I would give up on the valve.   There is a problem.   The turn valves are notoriously bad breaking like this.   It isn't that I don't think you could pop this open but why spend time working on something that is broke.  

I am not sure what the line is to the dishwasher - just guessing it is 1/4".  Depending on how much play you have I suggest unless you have a lot of plumbing experience that you install something like this.   Soldering a wet connection is hard, soldering a wet connection in a space like that is a pro job.   If you get the longest connector (sharkbite type - varies by store) you might be able to get by just cutting off each side, cleaning, and connecting.   

Also while at store get a 1/2" cap in case you have an issue and a release cup (sharkbite's cap is like $2 and release is like $1).   Always good to have a cap on hand so that you can turn your water back on when there is still an issue.