In order to have 2 ethernet cables, you would need to have two ethernet cards. Each ethernet card is hard coded at the factory with a MAC address (think of it is the serial number for that card). That MAC address is used by the Internet to uniquely identify your computer.
Since the two ethernet cards would have different MAC addresses, they Internet would see them as two different computers. The Internet would refuse to split packets between the two cards (as they are two different computers as far as the Internet is concerned), or to only send to one and receive with the other.
So while it is an interesting idea, the way the Internet is configured it would not work without special routers and switches that will cost you a fortune (about $3000 to start).
Even if it would work, you will hit a second problem. Usually the speed of you ethernet card is not what determines the speed of your connection. Most ethernet cards are much faster then the ISP to which you are connected. They limit the speed of your connection so they can cram more customers onto the same line as you. So even if you were able to add a second card, the ISP would still limit your speed and you would gain nothing.
Talk to your ISP. Usually for an additional monthly fee you can have them increase the bandwidth (speed) of your connection.