Modem phoneline connection problem.

I’m having trouble fixing an internal modem connection. Everytime I open my computer the phoneline hang-up(there’s no dial tone).When the computer is shutdown the dial tone comeback. To be able to connect, I use to remove the RJ11 to the box and place it back
instantly before connecting to the internet. When a dial-up connection has establish, I can able to use my internet. When the connection is cut, I have to do the whole process again to be able to connect. That means the internal modem is in good condition. How could I fix this problem?