Your problem could be one of three things: 1) The cable you're using may be faulty. Try a different cable and see if that helps. 2) The battery inside the controller may be faulty as well. However, they're easily replaceable. And the worst situation would be: 3) The USB port on the controller is indeed bad. You may need to get another controller and/or have your current one sent back to Sony for replacement under warranty (if it hasn't expired). I would try 1) first and see if it helps. If you go with solution 2), you may void the controller's warranty and you'll have to solve 3) by purchasing another one.
4GB of RAM is not enough RAM nowadays for Windows and applications. You should double that to 8GB of RAM, or max it out according to the specs of the laptop. The more RAM, the better.
A fast and easy way to upgrade your iPod's storage is to get an iFlash mSATA adapter and an mSATA SSD of your choice of capacity. I've done this with my iPod Video and now have 128GB of storage available (more to come down the road!)
I have a pair of Famicoms (both the original and an AV Famicom). They both happily accept the power adapter from either a US Sega Master System, or a model 1 Sega Genesis. This PSU has the correct barrel connector size, voltage, and pin orientation.
You may have a bad video cable. Get a replacement one and try it out. If it continues to persist, there may be either a failing component on the board (maybe the VDP?), or the connector itself for the AV cable is breaking or failing.
Have you managed to successfully restore your iPod using iTunes? That screen usually shows up only if your iPod's firmware is damaged in some way or another. A restore will usually get it working again, but if it still shows up even after a restore, your iPod may have another issue that may need higher up help.
You may have ordered a logicboard for a 2nd generation mini, which has a different LCD and connector. You'll have to now find an LCD for a 2nd gen mini, or find another 1st gen mini logicboard.
It sounds like the accelerometer in your nano's damaged due to the fall. Have an Apple Service Technician take a look at it. Unfortunately, I don't think you can easily replace this part.
Pulled the 40GB drive from my Mac Mini G4 and replaced it with a solid state drive (mSATA to PATA enclosure with a 120GB mSATA drive). Since my Mac Mini runs MorphOS instead of OS X, it’s been absolutely screaming; MorphOS booted in 10 seconds on the HDD, and now it’s “blink and you’ll miss it” fast on the SSD! :)
Pulled the 40GB drive from my Mac Mini G4 and replaced it with a solid state drive (mSATA to PATA enclosure with a 120GB mSATA drive). Since my Mac Mini runs MorphOS instead of OS X, it’s been absolutely screaming; MorphOS booted in 10 seconds on the HDD, and now it’s “blink and you’ll miss it” fast on the SSD! :)
Be *very* careful on the left hand side. It's almost too easy to scrape the click wheel cable and cause damage to it!
Please note: these screws can (and may!) strip easily, so take extra care in removing them!