An amplifier will not help. A splitter should never be used on DirecTV cables. I suggest you call either DirecTV or the
installation company and complain.
I assume you have an oval DirecTV dish. These come in several styles, all of which have 4 outputs. It is common practice for
installers to run only the cables actually required for an installation. And the installer was correct - the only solution is to run a cable from the dish to the receiver. DirecTV doesn't pay the installers much for a 'standard installation', so they try to make up for it by overcharging for 'non-standard' installations. Even so, charging even a hundred dollars seems excessive unless you have a very unusual setup.
If you are reasonably competent with hand tools, can learn to install connectors, and are not afraid of heights, running the cable is easy, particularly if you have a helper (it's even easier if you have the helper do the climbing, crawling through attics, etc.). Alternatively, check with your friends, neighbors, maintenance people at work to find someone who is capable of running the cable. Make sure they are familiar with satellite hookups.
PlainBill