It is possible to access it through any other computer, provided that you have the equipment to make it work. This, depending on the SSD, may be just a cable, or you may need some type of enclosure. You will need some type of device to convert a USB to the SSD connector so you can let the SSD communicate data with the PC through a USB interface. It is the same principle as with a standard HDD.
If you dont have the necessary items to make the connection, unfortunately the only other thing you can do is dismantle another desktop and connect the SSD to that computer as a secondary drive and look on that desktop. Keep in mind, you must already have a drive with an OS installed on the 2nd machine, and you cannot remove it, as you still need...