If the needle is really clogged, then you want to prevent the dried up ink from going to the print head or dampers. So if you are sure that there is a clog before the damper or the print head, then you are going to want to look at doing the following steps:
1. Disconnect the ink line from the damper.
2. Remove the ink cartridge and put in a cleaning fluid cartridge (or best case - put in a refillable cartridge with a mixture of warm cleaning fluid and distilled water. The warm mixture can help break up the clog).
3. Attach a syringe to the end of the ink line and draw the remaing ink in the tube into the syringe. You may have to do this a couple of times.
4. If you experience resistance, then you will need to get a refillable cartridge so you can push the ink in the opposite direction. I don't recommend pushing ink back into a closed cartridge because then the clogged ink particles will be in the ink bladder the next time you use that cartridge and you could put air into the cleaning cartridge. You could use an empty ink cartridge if you have one as well.
5. Once you get a good flow through the ink line and needle, inspect the ink line to make sure that there is no build up through it. If there is, you might want to consider replacing that ink line at this point.
Just be careful to make sure that the syringe does not disconnect from the line and the cleaning fluid spills into the printer if you are going to let it sit in the ink line / on the needle for a period of time.
You can also use a guitar string to attempt to break free the dried ink
If you end up not being able to get the needle cleaned and need to buy a new brass needle for your anajet, you can buy one here