@ p377y7h33f:
Welcome at Win-RAID Forum!
Obviously not. AFAIK your old Alienware laptop has an Intel ICH7 Southbridge. Only Intel ICH7R (Desktop) and ICH7M (Mobile) Southbridges do support AHCI. Furthermore the BIOS should have the option to switch the SATA mode to "AHCI".
Yes, there is a speed difference between SATA2 and SATA3 Contrillers.
Even a brandnew SSD may be faulty, but in this case you have the option to return it to the vendor.
If I were you, I would purchase a laptop with SATA3 and AHCI support instead of a new or used SSD for your outdated laptop, which doesn’t even support AHCI.
Regards
Dieter (alias Fernando)