because ON LED and Ethernet LED are flashing simultaneously, there is a problem with a power supply.
What kind of problem is a good question. It may be a problem with a power adapter.
It is better to find another 5V power adapter and check.
I agree with previous posts, the most likely problem is the power supply, are you using the one included with the Galileo card? (most of power supply problems I've seen are related to using a "similar" one, not the original). Make sure V and A are the required ones).
No, I am using an unofficial power supply, which claims to be 2A/5V. Thanks for the replies, I will try with another one.