Key press/Key release

I'm not surprised it's not working. Now, I don't know the slightest thing about VHDL, but I do know about programming in general.

Firstly: INDENT YOUR CODE With no indents the code is all but unreadable. Here is your code indented properly:

PORT (
    KEY : IN STD_LOGIC_VECTOR(3 DOWNTO 0);
);

SIGNAL A, B, C, D : STD_LOGIC_VECTOR(1 DOWNTO 0);

BEGIN
    A <= KEY(0) & KEY(1);
    B <= KEY(0) & KEY(2);
    C <= KEY(0) & KEY(3);

Readkey: process(KEY) 
begin
    if (A = 1) then
        D <= "00";
        if (B = 1) then
            D <= "01";
            if (C = 1) then
                D <= "10";
            end if;
        end if;
    end if;
end process;

Now you can see one major flaw in your code at a glance.

C being 1 will only be tested if B is 1, which itself will only be tested if A is 1. The if statements shouldn't be nested like that.

Secondly, (again, I don't know VHDL) is how A B and C are being assigned. In a classic programming language you would need to assign the incoming values to A B and C every time you want to test them, otherwise you won't ever see any changes. This may not be the case in VHDL, but it's something to look more closely at.

What you can do is create an idle state, and when you detect a button press you switch straight to the idle. Then you can have a counter in idle which waits for a while before you start scanning buttons again.

For example:

-- include numeric std
signal idle_counter : unsigned(31 downto 0);

      ...

      when state3 => 
        case bcd_val is
          when "01" => 
                Send <= '1';
                scannel_val <= "0101"; 
                fsm_state <= idle;   -- switch to idle
          when "10" => 
                Send <= '1';
                scannel_val <= "0110";
                fsm_state <= idle;   -- switch to idle
          when others => 
                scannel_val <= "0000";
                Send <= '0'; 
                fsm_state <= state1;   -- carry on scanning
        end case;
        idle_counter <= (others => '0');
        ...
      when idle =>
        if (idle_counter < some_timeout) then  -- some_timeout is how long you want to wait (in clock cycles)
           idle_counter <= idle_counter + "1"; -- increment counter
           fsm_state <= idle;                  -- stay here
        else
           idle_counter <= (others => '0');    -- reset counter
           fsm_state <= state1;                -- go back into checking
        end
        --scannel_val is valid here, so you can do something with it if you'd like.
        ...
      when others => scannel_val <= "0000";

There is one process in this code you've posted.

It starts with

scan_fsm : process (reset, clk) <= Sensitivity list
begin  -- process key_scanner

and ends with

end process scan_fsm;

The clock and reset are part of the sensitivity list. That means that this code is only going to be triggered when either clock changes or reset changes.

De-bouncing can be done in a separate process. Basically, you want to make sure that the button was pressed for a number of microseconds before it triggers. What we want to do is save the value of the input for a number of clock cycles. Then only register a 1 when the history has been constantly 1 for for the past 32 clock cycles.

Example:

-- these are our row inputs (to become bdc_val)
signal row1 : in std_logic; 
signal row2 : in std_logic;

...
-- this is our history vector
signal row1_z : std_logic_vector(31 downto 0);
signal row2_z : std_logic_vector(31 downto 0);

-- debounced signal
signal bcd_val : std_logic_vector(1 downto 0);

-- a whole vector of ones for convenience
signal ones    : std_logic_vector(31 downto 0);
...

ones <= (others => '1');

-- generate our histories
gen_z : process (reset, clk)
begin  
  if (reset = '1') then
    row1_z <= (others => '0');
    row2_z <= (others => '0');
    bcd_val <= (others => '0');
  elsif (rising_edge(clk)) then
    row1_z(31 downto 1) <= row1_z(30 downto 0); -- shift everything up 1
    row1_z(0) <= row1;                          -- save the most recent input
    row2_z(31 downto 1) <= row2_z(30 downto 0); -- shift everything up 1
    row2_z(0) <= row2;                          -- save the most recent input

    -- we only want bcd_val to be 1 when the entire row history for the past 32 cc is 1
    if (row1_z = ones) then
      bcd_val(0) <= '1';
    else 
      bcd_val(0) <= '0';
    end

    if (row2_z = ones) then
      bcd_val(1) <= '1';
    else 
      bcd_val(1) <= '0';
    end
  end
end