Is Arithmetic.dll in a location where it will get found ?
Were the functions declared with the stdcall calling convention ? (Not sure if this is still a requirement for dll's being accessed by Win32::API.)
Does Arithmetic.dll export the 'addNumbers' function ? (Running dumpbin /EXPORTS Arithmetic.dll will tell you.)
Is the dll functional when used from C programs ?

Another way to access the Arithmetic.dll functions is to use Inline::C (or XS) - though you'll need to have an import lib (Arithmetic.lib) for that to work, unless you're using the MinGW compiler. Trying to access the Arithmetic.dll functions using Inline::C might provide better agnostics if there's a problem with the dll itself.

Cheers,
Rob