The door switch on your Samsung dryer should make a click noise, you may have a dryer door switch that is faulty. Try using a multimeter to check it.
A thermal fuse might be faulty also. This is a cheap part and can be replaced easily.
It may be an issue with the control panel. If the dryer simply clicks, there may be an issue with control board.
Also, with your leaking Samsung washer, if you recently cleaned the filter, most likely, it was not installed properly. Remove it and check the seal or o-ring on it to be sure it makes a seal when you reinstall.
Let us know what you find...