This solution is not valid, there is no checking for wrong ships placement.
Try
int[,] field = new int[10, 10]
{{1, 0, 0, 0, 0, 1, 1, 0, 0, 0},
{1, 0, 1, 0, 0, 0, 0, 0, 1, 0},
{1, 0, 1, 0, 1, 1, 1, 0, 1, 0},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{0, 1, 0, 0, 0, 0, 0, 0, 1, 0},
{0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 1, 0},
{0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};

Should be false but your solution gives true.

Same problem.