Receive bitcoin before block downloading is finished here's the story: 

I've downloaded Bitcoin v0.8.5-beta and bought myself some bitcoins before the block downloading was finished. Now the downloading is still not finished (3 days and counting): 250k and a bit with a rate of 100 an hour or so. I' ve got a bit of an older computer so that's probably not helping. 

Question: will I ever see my bitcoins and/or is there another way to transfer it to another wallet? Or is there a way to download the blocks faster? 

I'm fearing that the rate of blocks created is higher then the download rate of my computer...
Please consider using thin client, like Multibit. Your balance will be available to you after few second. You can import BitcoinQT wallet in no time.