It is possible to upgrade the IcePipe A40 with a radeon 7750 silent videocard.
my bad , A typo
an i5 3550 if you wont overclock
a 3570K if you will
Usually graphics cards with passive coolers rely on the case fans to keep air moving past them . In a case with no fans I would be surprised if even a 7750 would run at cool enough temperatures .
And it wont game particularly well
Another option is to move the computer further away . A USB keyboard and mouse should work at a distance of 5.5 meters , and so will a DVI link to a monitor