Service tag not recognized by My Dell Downloads after new HD installation -- Can't access original install software -- refurbed Vostro 3360

I recently installed a new hard drive in my refurbished (now out of warranty) Vostro 3360 after the original drive suffered a fatal crash. I've been able to identify and install most of the drivers through the "Analyze System for Updates" feature. However, although this utility can detect my service tag and analyze my system, I cannot register the computer to access My Dell Downloads so I can reinstall software for the fingerprint sensor and webcam, as well as other third-party and Dell software that was originally installed.

Initially, when I attempted to register the laptop for My Dell Downloads, the process would just hang endlessly (no matter what browser I used). Following a tip I saw online, I checked my BIOS and found that the Service Tag field was blank, so I went ahead and entered my Service Tag number and updated the BIOS. Now, when I attempt to register the computer, I get a "Service Tag not supported" message.

I don't know if this issue is related  at all to the new HD installation since this is the first time I've ever had need to access My Dell Downloads. But, it has become an issue for me because of the installation.

Ugh. So:

1. Is there any way to get the system recognized so it will register with My Dell Downloads and access the originally installed software? Is there something I can/should do in BIOS? Something Dell can/will do from their end? (Even if I have to pay tech support to do it?)

2. If not, is there some other way that I can obtain the software to make my laptop fully functional again? I especially loved the fingerprint sensor for signing into my laptop and would hate to give up that feature.

Thanks!