"A USB Device is Drawing Too Much Power..."

I recently bought a small external hard drive that draws power from the computer itself (no external power supply). I was transferring files from a drive WITH an external power source to the new drive, and that error came up and the drive without a power source was ejected. So I removed the remaining drive and tried again with JUST the small external HD plugged in, and the same error message happened. So I tried again with the small HD with both USB plugs, and the same message.

Two things:
1. Now, when I plug it in it won't even register and the error message will immediately come up. But when I unplug the ethernet cord and try, it will register, but I haven't left it in for long enough to see if it stays. Is it possible that without the ethernet cord plugged in my MacBook will be able to maintain enough power to the drive to continue transferring files?

2. Last night I bought a USB hub with an external power source, thinking that this would solve my problem...thoughts?

Sorry if this is really confusing, I can answer questions anyone has if they're confused as to what I'm saying.

G'day and welcome to the forums.

The mains powered hub is the way to go if you must use USB. Macs do work much better with Firewire.

any resolution?

Just wondering if you ever found a resolution. I have the exact same problem. Was using an external CD/DVD drive, and now neither USB will work.
Of course, I fried my CD/DVD drive (my husband, without asking, plugged it into A/C power--it's supposed to run off of computer power!), and now I get the "USB drawing too much power" message, and neither USB will work.

Anyway, did you have any luck?

Thanks.

Normally, powering down the Mac and leaving it off for awhile will resolve this. If it doesn't, you might try resetting the SMC. See this LINK.