So, I thought I’d give Linux a try on my laptop alongside Win7.
Rigved Rakshit from भारत गणराज्य India
Your partition table is most likely corrupted. You can use GParted Live to recover the data on lost partitions. Then, you can fix your partition table by re-creating all the necessary partitions.
Based on the fact your laptop was unable to boot Ubuntu (without setting nomodeset, presumably) and unable to run Debian Live, it is obvious that you graphics chipset is not properly supported on Linux. But I may be wrong as I do not know much about you graphics problems. Have you tried asking about the graphics problems on the Ubuntu or the Debian support channels?