Honestly, though, I think you could get SAP or Oracle to have consultants for you on site free of charge to install and support their respective ERP systems, and it wouldn't make much of a difference. The problem seems to be one of personnel management.
Do you have a HR person on site? If so, they're clearly not doing the job. Even with pen, paper and manila folders, keeping a file on all 100 employees is fairly easy.
If you don't have an HR person on hand, someone should be designated as the 'owner' of this process, and clearly defined policies & expectations set forth.
That all said, here is a pretty decent site for finding smaller-scale enterprise software packages. If you scroll on the left, you'll see some personnel management apps. http://www.capterra.com/
Best of luck!