Do you have a jailbroken iphone? If do so you have have a tethered jailbreak and might need to use redsn0w to boot tethered now option. Theres a new tool to untethered jailbreak the iOS 5.1.1 its very easy and works on the 3gs whit no problems, and eliminate the need to connect tue iphone to the computer on every reboot.
I had this problem before, somethimes iphone go directly to Recovery Mlde when turned on, first thing to try whit the previuos/old battery to see if restore completes. If no, it may be unlocked before and its on 06.15 baseband thats why error 3914, so may use redsnOw pwoned dfu mode and restore whit a custom firmware, 4.1 always work, when working you can upgrade to latest firmware.
may be a loose connection on #3 connector, this one turns the lcd backlight off when on a call and its the earspeaker. sometimes get loose or misaligned on the reassambly process, open again and check.
It must be the digitizer went bad, sadly its kind of expensive around $70 for an OEM lcd and digitizer assembly as they come as one unit. Theres a guide how to replace the display assembly on a original iPhone and lots of videos on youtube.
You will need the power button flex replaced, and the part on the step 23 is the power button holder/braket it should be still attached to the old flex that you replaced. Search for iphone 4 power button flex