Should I mine bitcoins or litecoins? I don't pay for my own power, but I have two problems mining. I am CPU mining at 250 mhash/s because my AMD Radeon HD 7800 series graphics card will only produce 4.0 mhash/s (the other problem I'm having that I don't understand) but my main question is- what is more profitable to me? litecoin mining or bitcoin mining?
Litecoin mining is currently more profitable for likely all GPUs.

From the bitcoin and litecoin hardware wikis, you'd get 300-400MH/s for bitcoin mining and 340-470kH/s for litecoin mining if you set it up properly (and there is something VERY fishy about you getting 250MH/s with your CPU, I'd guess it is using your GPU though you don't know it...).  

For bitcoin, the current difficulty is about 6,500TH/s.  Thus, you'd own about 300/6,500,000,000 of the network.  At 25 bitcoins per block, 6*24 blocks per day, and $800 per bitcoin, you'd make about $0.13/day.  There is specifically-designed hardware for mining Bitcoins, which is way more powerful than GPUs, so unless you can buy a dedicated mining ASIC, your energy bill would overcome your revenue.

For litecoin, the current difficulty is about 90GH/s.  Thus, you'd own about 340/90,000,000 of the network.  At 4*6*24 blocks per day, 50 litecoins per block, and $25 per litecoin, you'd make about $2.72/day.  It uses a different algorithm (called Scrypt) than Bitcoin. FPGAs and ASICs can't be optimized for this algorithm as much as they can be optimized for Bitcoins' algorithm, so Litecoins are mined exclusively with GPUs. This means that you can still be comptetitive, and you should mine those.