Fuel Problem

I have the battery charging and I will recheck power to IFS in the morning, but I am pretty sure I am getting no power there. However, the battery was getting weak when I started checking things then it just went out completely.

Ok I put a brand new battery I just bought for my mystic. It sounds like fuel pump is kicking on to prime now. I also changed the fuel filter it was very bad. Aside from that I put fresh gas, seafoam, and octane booster. The car will run but the minute you let off the gas it kills and the battery light and check engine light come on. I have put a code reader/scaner tool on it and no codes are coming back. I have also changed the tps. Fuel pressure under the hood is better 38-41. Could the alternator be bad and not sending the right voltage for it to idle? The new battery died one time but i jumped it off and it has been fine since so I don't know if it wasn't fully charged when I got it or if maybe it was a bad connection. All fuses under the hood are still fine and number 34 in car is good also. I just don't know what could be causing it not to idle.

Got it running again. I think it was a combination of things. The battery is not even a year old and bad again. I think I have had it with Interstate batteries. The battery goes out once a year since I bought that interstate battery. So I guess it didn't have enough juice to prime the fuel pump. The fuel filter was clogged with some nasty stuff so I put a new one on. Next I cleaned the IAC valve and throttle body real good. Lastly, I changed the PCV valve. Fired her up and she is running like a charm again. Thanks for all the help guys.