The PSTwo has two door sensors. Nothing will spin if it thinks the door is open. The first and least likely to fail is a little black nub right above the power switch. It must be pushed down. The second is way at the back, to the back left of the laser assembly, and is a white or brown plastic box with a tiny plastic nub sticking up. It needs to be down as well. Easiest way to test is to remove the lid altogether, and manually press down both sensors, because you can access them both easily. Have a disc in, turn it on, and press down both sensors. If it works, disable one or both of the sensors, and you should be playing in no time.
Your system is a PSTwo, not a PS2. Check to see if the sensor on the PSTwo laser is broken off, or stuck down or up. It's a tiny black nub on the surface of the laser closest to the transport (disc spinning motor). It's supposed to freely push in and pop back out. It's easy to make it stuck if a sticky liquid gets in there. Good Luck.
Or a USB key. If you have an older PS3, the memory card slots can do this also. However moving the PS3 HDD from one PS3 to another is possible, it WILL NOT do what you want. The new PS3 ALWAYS insists on a format of the new drive prior to using it, erasing all of the data you are trying to save. Good Luck.
Did you perform the correct sync of the remotes with the console? You make no mention of it. It's described in the owners manual. On the Wii (while powered on) flip open the little rectangular door on the front. Press the red button. Immediately after that, open the wii-mote battery compartment and do not remove the battery. Press the red button you see there. Then press A on the Wii-mote. The first little blue light should come up on the wii-mote. Lather, rinse, repeat. Good Luck.
Will it work reliably motionless, say running on a flat surface with no one touching it? If it does, you likely have a faulty ribbon cable in your hinge. Once they get touchy, they get so twitchy as to be unusable. We fix those by replacing the entire top half of the DS, hinge top screen and all. Going inside the hinge is VERY labour intensive. Plus that twitchy ribbon cable is wave soldered to the top screen anyway, and cannot be removed from it. Hopefully I'm wrong, because that is not an easy fix, and requires a donor DS Lite. Good Luck!
Audio can cut out based on heat stress issues on the motherboard. I've seen it numerous times. The heat stress usually causes 3 red lights, but it can do this. Complain loudly to MS warranty (1 800 4MY XBOX). The answer above mine is worth a shot of course, try that first.
I run OSG and we don't fix 360's that old. The X-Clamp method does work, at least 65% of the time. And 50% of the time it will work for more than a few months. It is not what we would call a reliable fix. But if it's your own time, and you spend little on the kit, you've got little to lose. Just remember this, you are doing a quick fix on a design related heat fault, on a unit with a DVDrom drive that is more than 4 years old. (the DVDrom lifespan averages 4-6 years). I'd use a unit like that in shop, but I'd NEVER let it go to a customer. Good Luck!
I'm with 'beyond repair' above me. That said if your time and efforts are free to you, you have only the cost of parts to worry about. I would recommend a limited approach, as the salt walter tells me 'reliable' may not be in it's future if it works at all. My definition of limited approach- try the battery. If that does not work, STOP. One could go down the rabbit hole on this one, buying part after part, until you were better off just getting a cheap 3GS.
You need to be able to isolate the issue. It's either a failure on the backlight of the screen necessitating a screen replacement, OR it is a failure of the circuit that powers the screen's backlight on the main circuit board. If it's the latter, you may need a new mainboard. My best guess is the latter. If it was mine, I'd likely use it as is, as repair may be more trouble than it's worth. However, if time and parts money are no object, a screen replace has a chance of working, but a less than 50% chance by my estimation. I've repaired hundreds of iPods. This is however, my guess, and that's all it can be from your description. Good Luck.