Yes, when upgrading PT3 you already have postgres installed, so there is no need to install it again (and as you've seen this will cause problems). [for other's benefit, more than your, sorry]
I'm not a postgres expert, so I won't try to untangle your double install as I'll likely get you to break something, but here are a few people on this forum who will be able to help you.
I suggest you
start a new thread in the postreSQL forum please, rather than using this general Beta13 thread.
In your new thread...
Until the experts arrive, we can try and backup your database.
If you look at Task Manager / Processes, do you have any postgres.exe processes?
If not, try Start -> Programs -> Postgres -> Start service. Does it start? Are there any postgres.exe's now?
If so, postgres is running so we should be OK. Then you can backup your DB either using PGAdmin's backup/dump function, or see the command line way here:
viewtopic.php?f=17&t=8255