Yes, you can file a reopen claim; the issue would be...Whether new and material evidence has been submitted to reopen a claim for service connection for a left ankle, bilateral knee and neck condition to include pain.
You can get a Dr to state that it is highly likely that your left ankle injury incurred on active duty. The Dr must state that you provided him with the history of the event. If you do not have copies of your military medical records, I would suggest that you contact your nearest VARO and submit a letter to the Freedom of Information Act person at the VA and request copies of your medical records. Take the records to a private dr for review and this should help him link the problems that you are having now to what transpired on active duty.
A reopen claim is 2 parts; you must submit evidence to reopen and the new evidence must be sufficient to reopen the claim; something that is not already in the records. During this time, the VA cannot review records that are already in your claims folder concerning your ankle, bilateral knees and neck disabilities.
If the VA considers the new evidence as sufficient, your claim will be reopen and at that time, all the records in your file and be reviewed.
Also, submitting letters from people who you told of this incident can help. Make sure that they just talk about the symptoms; stay away from diagnosing the condition.
If the VA continues to deny your claim, request a formal at the BVA and provide testimony to a Board Member regarding the incident on active duty.
Oh, I can't understand why you were not given an exam when you filed your claim.