The issue admin 404 page not found usually appears when database was moved and it loses integrity keys. Also it may happened when you migrate website to different hosting.
You will not notice that issues exist until you will try to login to magento admin page. The magento admin 404 page not found issue will be shown in this case.
The issue will show admin 404 page not found and it doesn’t mean that this page not exist. if you will check Magento admin log ( you can find it at the magento root folder var/log/system.log ) you will see lines which reporting this issue.