The signal is split, whether you have a connection on the post or not. On a two-way splitter, you will lose more than half the signal automatically (the split, plus the "insertion loss").
You mentioned "-3.5db" per leg --- 3db = half (or twice, depending on the operation). A three-way splitter can be up to -7.5, sometimes more ... that less than 25% of the original signal strength (almost down to ~1/8th).
Every connector, every kink, twist, brusie will take it down even more.
Chances are you have either a flakey connection (oxidized or poorly terminated) or a poor signal strength to begin with. If you call the cable folks, they will send a person with a field strength meter who should be able to adjust the signal strength to the desired level, splitters and all.
As a last ditch, I'd say to disconnect and reconnect every device between where the cable come into your house and your computer. While it's disconnected, look at it to see if it looks dull and / or corroded. If it is, replace it. You should be putting in something that will pass up to 900-1000 Mhz with the losest loss you can find ... which will be 3.(something) on a two-way split.
DO NOT use a three-way (or more) splitter if you only use two ... the signal is dropped to each connector whether you use 'em or not.
Another way to go is to put a two-way at the entrance; one leg directly to the cable modem, the other to the TVs, split any way you need it (with amps, if necessary at the original split).
Good Luck
Scott