On my MacBook Pro 15", Mid 2012, there is a new option for dragging with three fingers in Mountain Lion. You place the pointer on the window title and use three fingers to move it around. As soon as you let go of the track pad it releases the window. To make the window stick to your pointer you tab twice with three fingers and tap again to release it.
Important is that activating three finger swipe gestures for Expose change to four finger swipes.
Before you do anything hastily, try resetting your NVRAM: https://support.apple.com/en-us/HT204063
This will clear several hardware-related settings and may resolve your situation.
If not, try creating a bootable installer (https://support.apple.com/en-us/HT201372), boot from it and check if your trackpad works there. If it does, backup and reinstall your OS.
The alternative would be to open up the device and check if the trackpad connection is properly attached. Sometimes (although very rarely) the plug can become loose, likely due to radical temperature changes. You should only attempt this if you're comfortable with electronics repair and following a guide on a site like iFixIt. They also have parts for self-repair.
If the latter doesn't help, sometimes disconnecting the battery and reconnecting it works, as this will clear any battery-buffered settings remaining.
In case all else fails, I suggest purchasing a replacement part through iFixIt and following a guide to exchange the trackpad – if you're at all open to self-repair. Having it exchanged by a shop is always going by to be vastly more expensive. The upside being that they're usually required to provide a certain warranty period for repairs. This is not a complicated repair, so you may want to try it yourself.
Best Answer
Is it possible something got stuck or is otherwise jamming the trackpad? Best bet may be to have genius bar take a look.
On older macbooks there was an physical adjustment you could make on the trackpack (open the case, remove some stuff, adjust screw). And we had a problem with the battery swelling which caused the trackpad to stop working (essentially prevented the "click" action, as it was pushing the trackpad up).