I have the problem that my RS232 always is sending data to the PC

you should only assert start when clockdiv == 0 AND [some signal which indicates you have something to transmit and want to transmit it]. Else, the cycle pasted below will keep looping forever.

always @(posedge clk)

begin

case (state)

4'b0000: if (start) state <= 4'b0001;

4'b0001: if (serclock) state <= 4'b0010; // Start bit

4'b0010: if (serclock) state <= 4'b0011; // Bit 0

4'b0011: if (serclock) state <= 4'b0100; // Bit 1

4'b0100: if (serclock) state <= 4'b0101; // Bit 2

4'b0101: if (serclock) state <= 4'b0110; // Bit 3

4'b0110: if (serclock) state <= 4'b0111; // Bit 4

4'b0111: if (serclock) state <= 4'b1000; // Bit 5

4'b1000: if (serclock) state <= 4'b1001; // Bit 6

4'b1001: if (serclock) state <= 4'b1010; // Bit 7

4'b1010: if (serclock) state <= 4'b0000; // Stop bit

default: state <= 4'b0000; // Undefined, skip to stop

endcase

end