You can sure try a slower speed.
You are saying that the copy that you downloaded (not the version you watched on youtube) is in sync and it was the burning process that threw it out of sync?
If so you can check your download and see if the audio portion was encoded using a VBR. Sometimes that can throw it out of sync on burning. If so you can use something like VirtualDub (free) to re-encode the audio portion using a CBR and try again.
I would guess that YouTube transcodes uploads but I have never bothered to check the characteristics of the formats that they use.
If it turns out that your downloaded version is also out of sync the same program can be used to re-sync it. Google would undoubtedly show you scores of site with step by step instruction on using it for the purpose.
Maybe I should note that you can not just check the beginning of the video. There are two main ways for the audio to be out of sync. One is audio displacement where the audio is shifted by the same amount through the whole video. The other is stretched where at the beginning of the video the sync seems decent but as it plays on it gets increasingly out of sync. The fix is different for each of them. Again plenty of people have written step by step instructions correcting them with VirtualDub. I am sure there are other choices too and that is just the one coming to mind at the moment.
As Felix says, it may be easier to just find a better copy because depending on where the problem first originated it could end up involving stripping the audio from the video and adjusting its run length in an audio editor and reinserting back into the video.