Cisco – What do all solid amber lights mean on a Cisco 3750 switch

According to http://www.ctrlink.com/2006_07_01_archive.html there is no minimum length when using a star topology (one node connected to each port of a switch). In the older times, when you had an Ethernet ring, there had to be minimum distances between devices to prevent impedance problems on the ring.

Concerning the low power mode, are you sure that isn't related to POE? I don't see how you can lower the power and still meet the guideline for voltage. Based on the impedance of the cable, the power consumed will be directly related to the voltage put on the cable by the NIC... See Ohms law, which isn't perfect when you are talking high-frequency waveforms, but the same principles still apply.

If booting while MODE is held down doesn't produce any output via the serial console, and you have the right cable and terminal settings for your device (which you should be able to find from cisco), then I would tend to blame a hardware issue.