Uninstalled last month, got banned today

So the last time I played (3/26, Vayne in nexus siege) I uninstalled the game that Friday so I could install and play some other games I hadn't for a few years that take up serious hard drive space (It was a payday and I no longer had physical copies of the games, had to buy them through origin) I open up my e-mail today to find that surprise my account has both received disciplinary action and been banned indefinitely with both e-mails arriving at 4:02 am this morning. I go to try and log onto the website so I can see if maybe my login info is no longer good (apparently not, I had to change my password) and find that someone played four matches on my account from April 2nd to the 22nd, in game modes I usually stay away from (I play almost exclusively co-op vs. AI, sue me). I have never shared my password with anyone nor signed onto league in public and I don't have my password written down anywhere, meaning someone took control of my account. From my understanding the Instant Feedback System's ban is irreversible, but the "My Account is Suspended" page says I should file a ticket with player support if I believe my account was compromised. I'm posting here because I don't know what to do going forward, (or where to file a ticket) the account is several years old and while I've never spent a penny on this game, I am fond of the summoner name attached to my account and have several champions I would not want to spend time regaining on a new account. Do I cut my losses and abandon this game, or is there any hope?