I recently repaired a samsung tab that had your problem. The miniusb connector connects to the main board via a flex cable, in my case the mini usb was damage so there was an open circuit on the 5V line, you can get another flexcable online for around $7 so its worth checking this out. You need a certain skill level to do this but use ifixit for a step by step guide on how to open up your unit. One question also is your tab recognised when you plug it into your computer? You might also try a new or a known working cable to ensure its just not a pure cable issue
If you dont want to keep the sheild you can cut it off fairly easily with a pair of wire cutters - the sheild is very thin. There are two holes in the sheild and you can get the cutter to start there, then carefully snip your way round it to remove it. Be careful as you may delaminate the board if you apply too much pressure or twist too hard. A word of warning regarding heat, be careful as there is a battery on the board which you should remove if you decide to use heat. Also the CPU and FLASH device which are BGA type devices are actually bonded to the board with an epoxy of some sort.
According to this post: (Using PS3 from India in USA power supply is universal - but be careful and realise that you will have to use the HDMI connection and not the TV connection (England uses PAL system where as the US uses NTSC [never the same colour])
Whilst this maynot be the real solution which of course is to find out why the heatsink is not making good contact you could try something like Bergquist GapPad 3000S30, or GapPad 5000S35 to fill in the gap. This is a thermally conductive gap filling material specifically designed to fill gaps between chips and heatsinks.