The battery on your laptop is probably long dead. You can pick up a replacement battery from online resellers for around $45-100 if you’d like. That said, depending on your use, I would recommend investing in a new computer, as even after this repair, this computer is not capable of many tasks in 2019 and will be running insecure software that is exploitable and dangerous.
There is a fairly common RAM issue with the T30 models that causes the RAM sockets to come unsoldered from the motherboard over time, which would basically disconnect the modules from the computer over time. The easiest way to get around this is to just replace the motherboard entirely, but if you are more skilled with soldering, then it is an option to just resolder the pins from the RAM slot to the motherboard. There is some helpful information on the ThinkPad forum here that you may find a good read within. Good luck!
Have you tried putting the original CPU back into the machine and attempting to boot with that? Likely the problem is from the new CPU. I would verify as well that the new Pentium M CPU is compatible with the R40. What is the specific version of the Pentium M that you purchased?
This is actually quite a common problem for this generation of laptop from IBM. The T4x series have an issue with the internal GPU coming ‘loose’ from the motherboard over time, usually increasing the problem when you lift the unit from the palmrest area. The only way to fully repair this would be a reflow job or motherboard replacement, but many people have found temporary fixes by applying pressure to the GPU, etc. There is a good post about it on the ThinkPad Forums that I’d recommend checking out.
As far as I know, you will have to install iTunes on your computer and restore the firmware of the device with iTunes. It should be noted that you will lose all data on the iPhone if you use this procedure. 1. Plug your iPhone into computer with iTunes installed, and open. 2. Shut down the iPhone (hold power button and slide to power off) 3. With the iPhone off, hold the power button for three seconds 4. While holding the power button, press and hold the home button at the same time. 5. Hold both buttons for 10 seconds. 6. Let go of the power button, but continue holding the home button. After roughly 8-10 seconds, you should see a prompt in iTunes telling you that the connected device is in recovery mode and needs to be restored. From there, follow the prompts to download the iOS firmware for your device and restore it to factory defaults.
I would recommend going to a few local shops that could be in your area — try independent locations first. Avoid big-box chains like Best Buy. Go to a few of them and ask for some quotes. This should yield you a pretty good idea of how much to pay for this type of service. Although I would usually recommend doing it yourself, if you get it done by a third party, there will probably be a warranty attached to their repair as well, so you could bring it back and ask for it to be redone if it fails within that specified range.
Sounds like it could be a power delivery failure. If there is no power going to the battery or system itself, there will be no charging or lights turning on. The only other troubleshooting I could recommend would be removing the device from the charger, removing the battery, and holding the power button for 30 seconds while unplugged from both battery power and outlet charger power. Then, reconnect the charger (with battery still removed) and try again. If it works and boots up, then shut it down and reconnect the battery, and try again. Good luck!
Low FPS after leaving the charger is quite common. This is because when you unplug the charging cable from the outlet or laptop, it most likely transfers to Internal CPU graphics opposed to the far superior dedicated graphics card that is also present in your system. To enable dedicated graphics on battery power, open the NVIDIA control panel and switch the option to dedicated high power NVIDIA GPU. (seen in part in this video, here). If your computer is running slow opening software, I would first recommend running an antivirus scan with Malwarebytes, to make sure there is no malicious software slowing down your computer. After this, you can start closing software in the background, such as Skype, other web browser windows and tabs that are unneeded, and applications such as Discord that could be running in the background eating power.
On your model, I believe you must download the Asus AURA software from the Microsoft store before using the RGB backlighting functionality. You can download the software here: https://www.microsoft.com/en-us/p/tuf-aura-core/9nnfl39xkxdn