|Possibly it is the wrong type of cable for direct connection to the PC.|
There are two types. Straight/Patch which is used to connect un-like devices such as Modem to PC, and Crossover which is used to connect Like devices such as PC to PC or Modem to Router. Since this cable is used to connect from modem to router it is possible it is a crossover cable which will not work when connected from modem to PC.
The other possible reason relates to self-adjusting ports on modern devices which can sense whether the cable is patch or Crossover and adjust themselves to suit.
If the modem has a self-adjusting port it needs to be powered down between removing the cable from router & connecting it to PC. The auto-adjustment can only happen from a power-off state.
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