It appears the ampersand suffix still forces the constant to be of the Long datatype. But because a Long is 64 bit in .NET, conversions from VB6 have to be done with care. If the constant should be forced to be 32 bit (like a long in VB6), you have to use the % sign instead (the type character for an integer)

So the VB6 code:
Private Const STD_INPUT_HANDLE = -10&

should be converted to VB.NET like this:
Private Const STD_INPUT_HANDLE = -10%