LiPo battery charging question

I just bought something (used) that came with two LiPo batteries and a charger. The batteries are or seem to be completely drained (based on multi-meter). The charger has LEDs to indicate what is going on - Ready to charge, Charging, Complete and Error. The thing is that, when the batteries are connected, it won’t change from Ready to Charging. Is this more likely a battery or charger problem?

How old is it? I’d expect that type of problem after about 10 years or 400-500 charge cycles. The batteries don’t last forever. I use several thousands LiPo batteries at work, and after a while they just stop taking a charge.

Draining LiPo batteries to zero will wreck them.

As always, BatteryUniversity.com is an excellent source of information on batteries:
BU-409: Charging Lithium-ion
BU-808: How to Prolong Lithium-based Batteries
BU-808b: What Causes Li-ion to Die?
BU-810: What Everyone Should Know About Aftermarket Batteries

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