Well, I got a response from SQ via e-mail, actually two e-mails in one day. For some reasons, SQ comes across somewhat nervous.

Don't ask me why, I have no clue. Anyway, long story short, SQ agreed to reimburse for the full amount, $620 USD. I don't expect it to be this easy, all I said in my e-mail was this single sentence:
"Can you please explain why you are unable to reimburse for the full repair bill charged by the store for just over $600 USD?"
Then I signed my name. That was it. The contact person at SQ apologized yet again (seriously, there is no need to apolgoize 10 times for the same thing and frankly, even though I didn't intent to put the laptop in there, clearly, I share some responsbility for that stupid mistake) and then offered to reimburse the full bill. I never said I was unhappy about what they first offered. How they read that I was "unsatisfied" is beyond me. I was happy enough with how they handled it in SIN and their very prompt response to my letter, I really couldn't fault them anything aside by their obvious attempt to haggle over a small amount of money.
Trust me, I learned a lesson with this incident and I will make sure I don't put a laptop in the checked luggage ever again. It was really inconvenient to have an inoperable laptop on an overseas trip even when you have two, that thought alone is a good enough deterrent.
I hope when you read this thread, you have learned a lesson along with me. Even if you already know, it's like watching those in-flight safety video/demo again, it doesn't hurt. Now, I feel it's important to point out the disclaimer that SQ clearly states in their writing and I am going to quote it here:
"We have again reviewed and escalated your case to the higher authority since you are not satisfied with the offer. After a thorough review of your claim and considering everything, we are prepared to raise our offer to USD619.59 being full and final settlement to mitigate your loss. We would like to stress, however, that this is a goodwill gesture accorded to you under exceptional circumstances. We regret that we will be unable to accede to similar claim in future."
SQ insists on calling it a goodwill measure as opposed to repair & reimbursment. Obviously, they are covering their a$$ against similar claims in the future. I don't have a problem with that. Notwithstanding of course, there are at least 2 people in this thread who reported that SQ did reimburse for the repair. So what's SQ's official stand on this? I still don't know. They clearly go by the same rules as every other airlines, that is they can't be responsible for damaged electronics in checked luggages. But why they still do it? It's anybody's guess. I like to think SQ is a quality airline who goes out its way to treat customers well and I think they have demonstrated that.