[fastd]

We should know how the relay is wired; it's a traditional trigger and ground, with power in and power out, or is it wired some other way?
The blue light may not be wiring through the relay (I would think that it isn't).

I agree with Blas; I would replace the replaced relay first.

Since your headlights come on but go right back off, I would confirm that you are getting constant power from your trigger wire; I'd also just sanity check the power to the headlights to make sure the problem is not after your relay (headlight ground or harness issue).