If your modal popup is off the screen you could try moving the window.
Alt+Space will bring up the window menu and then pressing M will select move.
After this you can use the arrow keys on the keyboard to move the window. After you have used the arrow keys, the window may jump back to the mouse if you move it.
I was able to verify that the above steps work with the following example:
private void button1_Click(object sender, EventArgs e)
{
Form f = new Form();
f.Text = "test";
f.Load += f_Load;
f.ShowDialog();
}
void f_Load(object sender, EventArgs e)
{
((Form)sender).Location = new Point(-1000, -1000);
}