No you souldn't be hearing music without the battery hooked up. You have some serious problems going on (shorts, miswiring, etc.) which you need to fix before you go hooking this up to wall supplies, etc. Get it working properly off of battery first before you start messing around with other things. If this were working properly at the stock gain of 11, you will definitely know it, as full volume will be much louder than your ears can take.
In general, building and troubleshooting electronics involves narrowing the possibilities down by a process of trial and elimination. Go over your board carefully with a magnifying glass, comparing it to Tangent's instruction. Look for solder bridges, that you have the right component in the right place with good solder joints. Take voltage measurements of both the + and - pins on the opamp to make sure it is getting about 1/2 the battery voltage (+/- 4.5V when referenced to the virtual ground). Pull the opamp and ohm out all the socket pins to virtual ground. For example, the input pins (pins 3 and 5) should show your R2 (I think) resistor, or 100K ohms. Pins 2 and 6 should show R3, which stock is 1K. And so on. If they don't, figure out why and fix it.
From your picture, I can't see anything outright wrong on it, tho the picture is a bit fuzzy. You should have made sure the amp itself was working before you wired in a pot, etc. and cased it up, as those are just more varibles of stuff that can go wrong. Get the amp itself working, then put the pot in or whatever. Get it working right, then move on to the next thing.
A picture of the bottom side of the board would be helpful also.
good luck
