Can we convert matter to electrical signal so that matter can be transported on the internet

The short answer is "no".

To convert one form of energy to another you need a transducer (http://en.wikipedia.org/wiki/Transducer). A transducer is a device which can convert energy of one type into energy of another type. A microphone is a transducer because it converts acoustic energy into electrical energy. A light bulb is a transducer because it converts electrical energy into light energy. At the present time no one has invented a transducer which can convert matter of an arbitrary type and form into energy nor has anyone invented a transducer that can convert a representative signal into matter of a corresponding type and form.

In addition, consider the following (http://www.astronomycafe.net/qadir/q388.html):
1 gram of matter contains enough energy to light 30,000 100Watt light bulbs for 1 year. Currently you would have no good way to transmit that much energy across the internet even if you could make the conversion to/from energy. Or if you simply transmitted the properties of the matter, not the actual energy, the receiver would have to draw 3,000,000Watts of power from the local power grid to recreate the matter you defined.

In conclusion, no, there is no way to transmit normal sized objects across the internet.

Wouldn't it be cool though?

Agreed!
*emails capuchin a snack*

Beam me up Scotty!