Colin King: Dell 1525 battery not charging

My wife's Dell 1525 Ubuntu laptop starting having battery problems last year and eventually we ended up with a totally dead Li-ion battery.   Fortunately I was able to acquire a clone replacement for about £25 which charged fine and worked for a week before becoming totally drained.

According to some users, this happens because the charging circuitry has died, which was a little alarming since the machine was way out of warranty.  So I had a machine that runs fine on AC power, but the battery won't charge.   So I slept on the problem and this morning I thought I'd try another spare Dell AC adapter just to factor out the AC power supply.  To my surprise the battery started charging, so I had to conclude the problem is simply due to a broken AC power supply.

So if the AC power supply is not charging, perhaps the original battery wasn't dead after all.  I plugged in the old battery, gave it an hour to charge but found it really was dead and useless.

I've compared the characteristics of the working power supply against the broken one with a multimeter and I cannot see any difference, which strikes me a little curious.   If anyone has any ideas why one works and other other doesn't please let me know!