I accidentally damaged my logic board with a screwdriver

It is hard to tell from the picture, but it looks like you may have actually broken the trace on the Logic Board which is part of a major ground trace. If you broke that trace there is no easy way to fix it since you would need to find someone with soldering skills that can jumper the bad spot. There should be other ground traces, but since this is a major one I don't know how it would affect charging.

As others have mentioned a defective battery is also another possibility since the quality of third party Lithium-ion batteries is extremely poor.

Yes, Faishal_malota.

Many service centers are closed.

This simply involves someone with a CMOS safe continuity checker: there are a lot of CMOS devices on that board that could be damaged by a "plain jane" battery and light continuity checker. Many better Multimeters have continuity checking functions (along with their Resistance [Ohm, Ω] meter function).

You simply need one that uses a sufficiently low voltage for its continuity tests.

As far as soldering, the hardest part would be preparing the surface: the traces on the board are covered in a plastic coating.

That coating needs to be removed, from the exposed side of the board, on both parts of the trace, so a small wire can be soldered across.

The soldering needs to be done by someone with reasonably good skill, so the board and traces are not overheated.

So. Not trivially simple, but doable.

However, it simply begins with checking the continuity, there. Because, it is possible that you need not go as far as soldering.

(On the other hand, the width and hight of that trace does suggest it caries a significant current! As HWTech put it, that "trace on the Logic Board" appears to be "part of a major ground trace."

Even if it still has continuity, it may have significantly more Resistance than the circuit was designed for!

This higher than intended Resistance could have a number of adverse consequences!)

Halliday wrote:

Additionally, Faishal_malota, what service centers you may have been able to contact (especially Apple Certified), probably don't want to "touch" this: too risky, too easy to have it "go wrong" (then, you, the customer, and Apple are unhappy, to say the least).

The only thing an Apple Store or AASP would do is to replace the entire Logic Board since it is damaged. Assuming the original issue with the laptop was just a bad battery and not some other part of the charging circuit, then any repair shop specializing in board level repairs should be able to deal with the damaged ground trace although a Mac specialist at board level repairs would be ideal.

Faishal_malota:

I can't be certain, so I would want to try a continuity test (testing to make sure parts of the circuit are still connected) on the metal line that goes right past the damage. (The damage looks like it may have "cut" that particular line.)

It is probably a ground line, and continuity may still be maintained by way of other ground connections.

I would simply want to double-check.

Additionally, Faishal_malota, what service centers you may have been able to contact (especially Apple Certified), probably don't want to "touch" this: too risky, too easy to have it "go wrong" (then, you, the customer, and Apple are unhappy, to say the least).

The bottom line is that it's up to you as to what you are willing to do. What you are willing to risk.

It looks like you struck the ground trace with your screwdriver pointed parallel to it. The point of impact is not wide enough to break the circuit entirely, but as Halliday stated, enough to increase the resistance. On the other hand, if the screwdriver had struck the ground trace perpendicularly, then the width of the impact would have been long enough to cut through the trace entirely, which would warrant board repair. Overall, you should be fine as the circuit is still somewhat completed; however, if you experience any difficulties or slowdowns, you may want to consult a component level board technician.

You have nothing to worry about :). That only appears to be minor cosmetic damage; nothing that will affect the functionality. The different battery could explain the longer charge time.