Those cotter pins with the shield over them were part of the shipping braces from when it left the factory and they do have no bearing on the suspension system.
What most likely thats causing it to vibrate so badly are the cresent shaped plastic peices that fit between the plates under the outer tub,Their is 2 types of those on the washer one fits under the bottom plate and one fits on the top of the bottom plate andin between the upper and lower plate. They are impregnated with teflon and have worn out so instead of the plates sliding free the are grinding against each other
Those parts are called suspension pads,the part number for them is 285744 &285219 they can be purchased at your local appliance parts store or online at
This link shows where they are they are item numbers 13&15 http://www.searspartsdirect.com/partsdirect/part-model/Estate-Parts/Washer-Parts/Model-ETW4400SQ0/3191/0153200/W0607071/00005?blt=06&prst=0&shdMod=ETW4400SQ0