Also post your upload signals.
Those download signals are really low and you have some massive correcteds/uncorrecteds. A faster speed package and/or a replacement modem will NOT fix coax issues. You have loose connections, damaged coax, failing amps, etc.
Please describe your connection to the modem from the main line coming into your house, how many splits, etc.
Can you eplain the amplifier/spltter configuration a little better? Does the amp simply have multiple ouputs or does the amp feed into an independant splitter? Can you read a model number off the amplifier?
Be sure the incoming line is connected to the amplifier input. Take the amplifier output and feed it directly into the modem. (If there are TVs involved, leave them disconnected for this). Confirm the amplifier is powered. It should be very slightly warm. Let the modem connect and post the new signal levels.
Probably need to get a "clean" snapshot of your raw signal levels... well, as raw as can reasonably be done. The SnR values demonstrate there is a good bit of noise present, on top of the signal being weak. The amp could be failing or misconfigured (gains may need to be adjusted, power supply could be too weak or injecting noise, etc). There may be too much loss from splitters as well.
Get the amp and all splitters out of the line... make this a dedicated run to JUST the modem. May need to pick up a couple barrel couplers to do this... should be able to nab a pair of them at the local Wal-Mart or hardware store on the cheap.
Need to get some baseline measure of the potential quality of signal to the modem with as many impeding devices taken out of the loop. Then recommendations can be made on how to best feed signal to additional devices as needed, as well as ways to amplify/attenuate signal if needed.