I live in a house that has funky pre-1990 coax runs. In order to get my cable modem to work, we were limited to 2 rooms in the house, and we had to drop one of the splitters. Now anytime there is work done in the neighborhood, I almost always lose my connection and have to call in to have them rejigger (technical term) the load coming to my house.
Anyway, all that is to say that during the initial install, the tech told me that each splitter only affects the lines coming off the splitter, so the ideal place to have the splitter is as close to the de-marc, then dedicate one line for the cable modem. The standard splitters degrade the signal by about 3.5dB. The other thing to watch for is whether the splitter is able to pass the higher frequencies since the data portion runs in the higher frequecies.
If you're forced to use an amplifier (which the installer tried), you need to get one of the ones that is rated for two-way communication. One of the problems with these amplifiers is that they also degrade the signal getting to the cable modem, as well as the signal coming FROM the cable modem. Most cable modems put out a max of about 57dB of power. If you barely get a signal, putting an amplifier to boost your receive signal can add just enough degradation to the send signal that the 57dB is no longer enough to get sync on the provider's end. Depending on the model of cable modem, you may be able to check the power levels of your modem from whatever interface it uses. For example, I seem to recall that my cable modem (Motorola Sufboard 4100) was putting out 56 or 57dB or power, which means that if I add another splitter or amplifier in the cable modem path, I no longer sync.
Now, I do not work for the cable compaies, nor do I know that much about cable modem technology, so take all this with a grain of salt.