It could be very risky to run a 4870 in that computer.
First of all, there is almost no room, and i highly doubt the card will even fit inside the computer.
Second of all your powersupply is a risk to the computer and the card since it is 50 watts short.
Third, heat would definitely become an issue since there is almost no airflow in that case, and with a powerful gaming card like the 4870 heat would no doubt become a problem.
I am sorry to tell you that it is not worth the risk to install a 4870 into your computer, either get a better case/computer all together, or return your 4870.