Sounds a lot like a component problem, not so much like a shorted trace, etc.. Especially since it works for a few minutes intermittently. It can be tough to find these types of problems.

Start by using your senses: Touch, sight, smell to look for clues. Overheating or very hot components can sometimes be found by touching them briefly (Please be careful, sometimes components can get very hot) or looking for signs of brown/burnt components such as dark "rings" on ICs.

You can remove D23, and that will completely remove the battery memory retention circuit from the equation.

If nothing is found then I usually start by removing socketed ICs to see if any of those are causing the problem. After that it starts to get tricky. A lot of ICs are usually soldered in, and there are other components connected to the 5V rail. There's techniques you can use with more sensitive DMMs or specialized instruments. There is a also a technique of slowly ramping up the supply voltage until the culprit cooks - it's not an elegant way to find the trouble and can be risky, but it sometimes works.