To know 100% that it is hardware related, you can create a bootable version of linux something like mint: http://www.linuxmint.com/download.php if you have the same issues in mint you know it is the hardware.
It does sound like a hardware issue to me. Try dusting the buttons out with canned air this sometimes works. If it does not, the replacement buttons are generally very cheap (this is an example I am not 100% certain this will work in yours, it is best to take it apart and use the dell PN on the part) http://www.ebay.com/itm/DELL-Inspiron-N5010-M5010-Touchpad-Mouse-Button-Click-w-Cable-56-17501-601-/360818503072?pt=LH_DefaultDomain_0&hash=item5402756da0
If you do not have experience disassembling a computer entirely I recommend taking it in for this job. Also the cheaper solution and fastest would be to go get a wireless usb mouse...
By the way, windows allows you to switch what buttons on the mouse do: you could change the left click to the right click button.
Edited by zingo156, 10 February 2014 - 08:57 AM.