Do you want to take total control, not do anything that the remote selects or controls?
I think you can cut four traces and connect them to four pins configured as outputs on the Arduino, along with a fifth wire to provide a common ground, and directly control the brightness of the R, G, B and W elements.
A different kind of fun would be to recreate the IR control signal, and let the Arduino take the place of the remote. That would allow you to do what each key on the remote control does. This has the advantage of leaving the real remote control operational, and involves less cutting traces and pesky soldering.
But that would limit you to what the remote can do now.
I remove the chip and solder the connections to the Arduino as show in the picture?
Is the yellow cable connection left as is?
And what about power, can the Arduino by itself power this? This originally takes 3 AAA(1.5V) batteries. That's why I got the 4.5V power supply. Should I not use it?
Trace the yellow wire, is it the wire providing 4.5 volts from the battery pack?
The Arduino cannot provide the power, only the control signals. Yes, you should be able to use a 4.5 volt power supply.
Post a picture of the bottom of the circuit board.
If you can, measure the current when the lamp is providing the brightest whitest light it can - the power supply should be rated for that current plus a bit of headroom.
If you can't measure the current, say. There's another way to get at the answer. You would need a voltmeter.
Just use batteries for now. I would say that no matter you have a power supply or a voltmeter or anything, it will be the most safe and the power issue can be a second step.
The classic sketch blink.ino can be used, just provide the common ground and instead of wiring to a resistor and LED, you snake a wire from the sketch's output pin over to one of the channels R G or B.
BTW I note that you have red, green and blue wires and both you and the manufacturer seem to have placed them different to the labeling. No matter, it may be the labels that are wrong… naturally there will be a few surprises like that, all down to software.
Proceed with caution or not until another cycle or two here with anything more you can tell us.
It occurred to me that another way to hack this might leave you with exciting (!) options.
Remove the four surface mount resistors labeled 4K7 and place your wires where the left hand side of them was attached, leaving the pads that no doubt lead to the chip unused.
Do not remove that chip. leave it there where it will still be doing its thing or thinking that it was anyway, and one day you might could listen to what it says and get the remote back into operation in some capacity. The power it consumes is negligible.
Google for removing the SMD parts. Removal is easy and will take some care but no special tools. The main goal would be to do without damaging the pads.
You'll need to acquire and use four 4K7 regular 20th century resistors to use between the pads and the corresponding Arduino pins. I hope it is obvs that you have just externalized that part; the circuit remains the same. Output pin, series resistor going to the transistor cod trolling controlling the channel.
ok I have updates. Thank you @alto777 so incredibly much. Your comments were of extreme help.
I have 100% solved the controlling the light with my Arduino. I even modified an RGB library to work with RBG+W and it works great.
All I had to do is connect the cables as in the last picture I uploaded. I didn't have to remove the chip and the yellow connection I just ignored, I still don't know what that's for.
Next: power.
I'm getting a multimeter tomorrow from Amazon and will be able to make more experiments and understand this better. I'll test with batteries before power supply as you said.
Thanks for the report. Too often we get ghosted. I'm prolly not the only one who just forgets all about ppl. I assume they go away happy.
Did you land up removing the chip? I can't tell from the photos. I only care because I thought it was luck that allowed your signals to override those from the chip, therefore the various suggestions I made to get around needing to do.
if the chip wanted one colour to be on and you wanted it to be off or vice versa, one of those might be problematic.
Post anything you come up with if you've gone beyond test sketches. You can use analogWrite() directly to PWM control the brightness in case you hadn't realized.