I fired up my Pokémon HeartGold a while after I completed Pokémon White, & started collecting up Pokémon to transfer, unfortunately I don't know that many people with DS's & most of them have lost theirs. So I'm stuck with my old save file waiting to have loads of Pokémon transferred, just like Heathrow airport during an ashstorm. So I need some advice, should I wait until I've found someone who's willing to let me use their DS or should I restart completely? If there is a help, section just notify me please.

I remember I had the same problem, so I used the GTS. At that time, I needed to transfer 6. Out of them, I was fast enough to get 5, while the 6th was taken before me. So yeah, there is a risk.