I posted this question earlier in the day. After toying around for a little while, I figured out that my Windows 7 repair disc couldn't detect my HDD. I ran boot repair and restored the MBR. Windows 7 would boot, but Ubuntu would return
invalid arch-independent ELF magic. After receiving that error, my computer would only boot to a non-GUI grub menu. I'm really not sure whether it's possible to restore my setup.
System: Alienware m14x r2
Secondary memory: 750 GB HDD, 32 SSD for caching using IRST with Windows
Operating Systems: Windows 7 Ultimate SP1, Trusty Tahr
Partitioning Scheme: 100 MB system reserved NTFS for Windows, ~200 GB NTFS for Windows, ~350 GB NTFS storage partition, 50 GB ext4 Ubuntu partition, 32 GB swap