Get Deadly Premonition, it's pretty much based on the best Mystery series of the '90s (Twin Peaks... oh my god what a show!!!), and it's got an insane wacky factor, it will both creep you out, make you laugh, and get you intrigued. I dig it so much I imported a Japanese copy for my PS3 after seeing my friend play it on his 360.
Also if you ever find a cheap PS2 pick it up, and then get your hands on Shadow of Memories/Shadow of Destiny. That game is probably my favorite mystery game and I'd wager it's exactly what you're looking for. You get killed, but then are offered a chance to travel through time to stop your murder and uncover it's age old source...
Also might I recommend emulating SNES on your laptop, it should be able to handle it easy and you can even hook up a 360 wired controller (or get the wireless adapter) to it and use it. As a big fan of mysteries in all forms all my life I actually found a lot of the better JRPGs on that system to use mystery plots, games like Chrono Trigger and it's sequel Chrono Cross are massive mysteries that you spend most of the game uncovering the answer to, while gaining more questions in the process until all the loose ends are tied neatly at the end (if you do all the side missions, which how could you not?!), and I can easily say the same about Earthbound, also that system had horror mystery games like Clock Tower.
Heavy Rain on PS3 is a great mystery game naturally, and then there's of course Rockstar with the obvious L.A. Noire, and the less obvious every other sandbox game they've made (because in every GTA, and in Red Dead Redemption a key part of the plot is unraveling the mysteries behind certain events. From who leads the crime in Los Santos to Niko's past to John Marsden's motivation and the truth behind it). Oh, and while I'm on Rockstar, the Max Payne series are Noir shooters, so yeah, a bit of a mystery, though a bit less subtle and a bit more pulpy.
I do wish someone would just make that natural leap and make a private eye game... L.A. Noire was so close, and it even has the exact formula right there, now if they just made the world a bit more open and stealthy with the ability to find random side missions in a number of places in addition to the main story which just waltzes into your office in a skimpy dress with a pout... It would be so good!!
OH! DEUS EX! Play the original and the new one. They're like the corporate future version of what I was just talking about. XD