Remember that when you read data from a serial port, you get all available characters - so if the device at the other end sends "a" followed by a new line, you will receive two or three characters, not one. So your test may not be workign because you are gettign too much data!
Have a look: use the debugger to put a breakpoint on the start of the method, and "break out" what you are doing to make looking at it easier:
Private Sub Timer1_Tick(sender As Object, e As EventArgs) Handles Timer1.Tick
If int = 0 Then
Dim read = SerialPort1.ReadExisting()
if read = "a" Then
and see exactly what you are getting.