If you exit all of your clients and use the site to clear the queue, it runs the exact same code that I would run to clear your queue.
One thing you could try: first clear your queue of work, then wait a few minutes… say, 15 minutes or so. Then start up just one of your clients, and submit a quick simulation. Keep an eye on the console window for that client – did it run the simulation?
Then close that client, and do it for each of your machines on which you are running clients. Is each machine able to run a single simulation without any trouble?
Then repeat this test but with a short batch simulation, e.g. give it about 150 simulations, but set the error target very high, set it to “quick run”, and use a DPS spec. That will be enough that it has to create multiple batches, but it should still finish pretty quickly. Do all of those finish on each machine without any trouble?
After that, try starting up all of your clients, and then submit a single simulation, see if it works. Then do the short batch again, see if it works.
Hopefully that information can help narrow down the issue.