Are you sure the splitter is amplified? A quality splitter will have a db value on it, (usually 3.5 per leg on a two-way...7db per on a four-way), but these values are how much said splitter PULLS OFF the line, not amplifies...the lower the number the more signal you have. Also, any amplifier will have to have a power source...if the splitter isn't plugged into an outlet then it's not an amp. The poor reception is due to signal loss on the tuner, and your modem works cause it's on the 3 leg. And Workin is right, it wouldn't be good to have more than two splitters between the tap at the pole and your computer, as the return signal is not amplified, (even if you did have an amplifier).
The only filters we use are high-pass filters, which block all return signal, (if someone has faulty wiring and its screaming back to the tap and affecting other customers), and we do not use them in conjunction with modems.
I'm a contract Online installer for Comcast.
-Rhi