You have two options:
a. Download the whole blockchain (~170gb);
b. Import your private-key in an SPV wallet and spend the funds immediately.
Option A:
1. Open Armory;
2. Go to the "Announcements" tab;
3. Click "Secure Downloader" on Bitcoin Core at the bottom;
4. After finishing the download, close Armory, install Bitcoin Core and don't run it (uncheck the "Run Bitcoin Core"checkbox);
5. Open Armory again and let it synchronize (it will take a few hours/days).
After finishing, you should see your coins.
Option B:
1. Go to your wallet properties;
2. Click "Backup this wallet" -> "See Other Backup Options";
3. Select "Export Key Lists" and click the bottom button with the same name;
4. A new window will open. Only check "Address String" and "Private Key (Plain Base58)";
5. Look for your address at the list and copy the 'PrivBase58' text right next to it.
This is your private key. DON'T SHARE IT WITH ANYONE.
Now download Electrum (
https://electrum.org/#download) and when creating a new wallet, select:
1. "Import Bitcoin addresses or private keys" -> Enter your private-key from step 5 -> Next;
2. Now you should see your funds;
I suggest you create a new wallet by going to File -> New/Restore. And following the wizard normally (Standard Wallet -> Create a new seed -> Standard -> Save the seed (DON'T LOSE IT) -> Set-up password, etc... Then, just move your coins from the first wallet that you created by importing your private-key to this one you just created (with the seed). Use this wallet instead of the one from Armory.
