As Mr.Snake has pointed out Redington is the best place to get your laptop fixed. At other outlets mentioned, they would ruin it more than fixing it. Redington office is located on the C-Ring Road between Gulf cinema and Muntazah signal on your right hand side.
A word of caution, you can get anything fixed there, but you need lot of patience, since this is the only authorized service center in Qatar(like many other things here) you need to get a token and sit in the queue then submit the laptop. Then following up is also a task. However the service is good.
Try your luck....