Start with a multimeter and a thermal camera.

Those are the only tools you realistically need without desoldering. A multimeter lets you check for shorts (like VCC to ground on the RAM power rail), and a thermal camera will reveal a chip getting abnormally hot under load — a dead giveaway for a shorted internal transistor.

An oscilloscope helps if you’re chasing signal integrity issues (e.g., missing data lines), but it’s overkill for initial diag. You’ll also want the board’s schematic or at least the pinout of the RAM chip, otherwise you’re just poking blind.

Without a schematic, even thermal imaging is guesswork.