MacBook Pro only charges with smaller MagSafe 60W My MacBook Pro 2.3ghz  i7 mid-2012 stopped charging and the light on the charger doesn’t show up anymore. 

I thought it was the MagSafe 85W and got a new one, but my MBP is still not charging. The light does not work on both the old and new 85W charger, and neither actually charge my MBP. 

However, I have a smaller 60W MagSafe that works ok. The light comes on and it charges the MBP.

What could explain this? 

The DC jack looks ok, but I wonder if that could be it? Or is it more likely to be a logic board problem?

UPDATE

I’ve also conformed this by using iStat - it shows that the 65W charger provides around 30W while both the 85W chargers do not show up at all.

UPDATE 2

I have also used pmset from the terminal window to check the power management. As suspected, both MagSafe 85W are not seen at all, it reports "no adapter attached". It only works with the MagSafe 60W.

The rawlog, with the MagSafe60W attached and then removed shows: 
AC; Charging; 57%; Cap=3748: FCC=6550; Design=6900; Time=2:02; 3028mA; Cycles=92/1000; Location=0; Polled boot=05/12/19 08:19:07; Full=05/12/19 09:15:17; User visible=05/12/19 09:18:17 05/12/19 09:18:31 No AC; Not Charging; 57%; Cap=3761: FCC=6550; Design=6900; Time=2:01; 3097mA; Cycles=92/1000; Location=0; Polled boot=05/12/19 08:19:07; Full=05/12/19 09:15:17; User visible=05/12/19 09:18:31 

The rawlog with the same MagSafe 60W detached shows:
No AC; Not Charging; 57%; Cap=3761: FCC=6550; Design=6900; Time=2:01; 3097mA; Cycles=92/1000; Location=0; Polled boot=05/12/19 08:19:07; Full=05/12/19 09:18:31; User visible=05/12/19 09:18:31

The only difference between the Magsafe 85W and the 60W is the output:
- MagSafe 85W: output 18.5V, 4.6a
- MagSafe 60W: output 16.5V, 3.6a

I have also replace the DC jack and still no luck.

Why on earth my laptop only works with the adapter that provides less voltage and amperage?
Try to do a SMC and PRAM reset. 

SMC, amongst others, controls power management of your Mac. From https://support.apple.com/en-us/HT201295:


  These symptoms might mean that an SMC reset is necessary:
  
  
  [...]
  The battery doesn't charge properly.