Finder Doesn't Launch on Start Up

Question

My MacBookPro has recently had problems with the power adapter and battery. Since this morning (25 November), the Finder does not launch at start up. That is, the desktop appears after a slightly longer than usual start-up time, but nothing appears on my desktop--neither the Hard Drive, nor any of my other files on the desktop--and the tool bar at that should appear at the top of the screen doesn't. The dock will appear at the bottom of the screen, but none of the programs will launch.
My battery is as old as my computer, about four months shy of three years. In the past month, the metal inside the power cord running from the block of the adapter to the computer seems to have burned apart where the cord enters the block (the insulation has not, however, burned away). Since I won't have the money to replace this until next month, I've used electrical tape to keep the cord close to the block. The battery's life has deteriorated, according to CoconutBattery, to about %80 of its original capacity. Also, in the past week I've noticed an electrical buzz when the AC was plugged in, and I was running my computer, but the batter would not charge (it would only charge when the computer was shut down, though the buzz continued).
Are the problems with my power and malfunctioning finder related? Is it more important to replace the power adapter than the battery, or must both be replaced at the same time? Is there anyway to get the Finder to work again without doing reinstalling OS Leopard? Could my computer need a new internal hard drive (I was able to run disk utility from the OS System disk, and it recognized the usual amount of space used and available on the hard drive)? I will be in Jerusalem, Israel until June 2009. Should it be necessary, will I be able to receive face-to-face support here?
Thanks in advance.

Answer 1

My MacBookPro has recently had problems with the power adapter and battery. Since this morning (25 November), the Finder does not launch at start up. That is, the desktop appears after a slightly longer than usual start-up time, but nothing appears on my desktop--neither the Hard Drive, nor any of my other files on the desktop--and the tool bar at that should appear at the top of the screen doesn't. The dock will appear at the bottom of the screen, but none of the programs will launch.
My battery is as old as my computer, about four months shy of three years. In the past month, the metal inside the power cord running from the block of the adapter to the computer seems to have burned apart where the cord enters the block (the insulation has not, however, burned away). Since I won't have the money to replace this until next month, I've used electrical tape to keep the cord close to the block. The battery's life has deteriorated, according to CoconutBattery, to about %80 of its original capacity. Also, in the past week I've noticed an electrical buzz when the AC was plugged in, and I was running my computer, but the batter would not charge (it would only charge when the computer was shut down, though the buzz continued).
Are the problems with my power and malfunctioning finder related? Is it more important to replace the power adapter than the battery, or must both be replaced at the same time? Is there anyway to get the Finder to work again without doing reinstalling OS Leopard? Could my computer need a new internal hard drive (I was able to run disk utility from the OS System disk, and it recognized the usual amount of space used and available on the hard drive)? I will be in Jerusalem, Israel until June 2009. Should it be necessary, will I be able to receive face-to-face support here?
Thanks in advance.