To figure out what is wrong on your system, I'd need to have the SecondLife.log...
However you say "Export bad everything but ALSA is uncommented": if "export LL_BAD_FMOD_ALSA=x" is uncommented, then it's flagged as bad !...
To use Alsa, you should have:
or, using OpenAL (may result in inferior sounds, on some systems):
You also say "No Pulse Audio installed": please note that with ALSA drivers, you also need a software mixer active on your system (Pulseaudio, or Esound (esd), or Arts, or Jackit daemons), else the first program grabbing the sound device will be the only one able to play sounds (and if, for example, you got voice enabled in the viewer, the voice client may grab your device, not letting it available any more for the viewer itself).
If, like, me, you don't like the idea of a daemon running in the background just to provide poor/laggy/mutually incompatible sound mixing services, you can install
OSS v4.2 instead: OSS is now OpenSource and got a built-in, transparent, zero lag, software mixer, rendering all sound daemons obsolete and useless. I recommend
building OSS from source (to avoid the force updating feature that kicks in every 6 months), but you can just as well
grab prebuilt binaries.