2 BSOD's and Commputer reporting 4kb in Bad Sectors

I need some help here. By way of background, I have an Aspire One D255E Netbook from ACER. I am running Windows 7 Home Premium 32b. Recently I have gotten at least two BSOD's (possibly more overnight as I wake to my computer on the log-on screen). When CHKDSK ran during boot, it reported 4kb in Bad Sectors.

Now the question: If I low-level format or zero fill the HD, firstly, will it fix the bad sectors? Secondly, when I do this, will the computer still be able to recognize my external CD/DVD Rom drive which is what I will need to use in order to re-install windows.

I already know that everything on the HD will be lost and I need to back all the importnant files up. Just need those two questions answered before I continue with this problem. If you have alternative suggestions that would allow me to keep my files, I'd be interested in hearing those too. Thanks so much!

By way of an update:

My little netbook stopped working. This morning, it froze. I didn't get a BSOD, however, it wasn't doing anything. It said my cpu was at a full 100% but my cpu light was blank. I ended up having to shut it down manually and now am booted up in safe mode.

I'm currently running my virus scanner and malware scanners to eliminate the possibility of that being the cause of the trouble. Can 4kb of data in bad sectors really cause all this mayhem? Is there a way to fix it? My wifi on my netbook isn't working anymore and I'm posting this via my phone (which is connected to my wifi - that's how I know its the computer and not the modem). I seriously need some major help here! Please windows geeks I'm begging you!

Hard Drive is failing.

Back up what you can and time for a new one.

Low Leveling will not fix bad sectors...it's dying!!

Boot sequence is set in BIOS ensure boot from DVD is 1st then HDD 2nd