My nokia 6500 slide doesn't turn on

your likely going to have to replace the battery on a device this old. Sourcing a known working battery for this is unlikely.

You can also power the phone with a lab bench power supply set to 3.7V and with a current limit of 400mA. If there are 3 battery pins, the unmarked one or T is the thermistor terminal; some newer devices need to see a resistance value of ~9-11k ohms here, but with cellular phones of this age, I am not aware of any.

Some older phones do not even need a battery to boot. If the device's board and screen work with a USB cable might be enough to power it on with the battery removed.

Hope this helps you relive the early era of cellular, and I hope you find lost and forgotten memories on your old device!