I was actually able to find and fix my problem on my own. For months, I had items showing up in the "Other Payroll Items" window that weren't a part of the employee's Additions, Deductions, and Company Contributions. One employee even had double Federal tax being taken out and I had to delete it on every paycheck. I stumbled upon the fact that these items had inadvertently been added in the "Other" tab in the taxes. This had to have happened during a update or power failure or some sort of other issue. Once I deleted these items, all my errors disappeared and I'm able to access Payroll Setup successfully. Check everyone's Other Taxes to make sure all items listed are correct!
