Computer either BSOD's after start-up, or runs fine

So my computer seems to have about a 2/3 chance of BSODing in the first few minutes of running. After that, I encounter almost zero problems, aside from some weird issue with Windows Update (I haven't been able to install any updates), but that's for another thread. The BSOD seems to show one of two errors, so I'll post both here.

Before that though, I also want to say that I did have some weird problems with this computer previously, probably due to OS corruption, but I'm currently running a very fresh install, with not a whole lot on it. The weird thing is, it still looks like OS corruption, and you'll see why in at least one of the two BSOD codes. The installation disc actually had a bit of trouble unloading its files properly, because it said files were missing a few times before installing. I have a friend who had the same issue with Win7 though, so I don't think that's as out-of-the-ordinary as it sounds.

Anyways, the BSOD stuff:
This one says there's a memory management error.

Code:

Problem signature:
  Problem Event Name:	BlueScreen
  OS Version:	6.1.7600.2.0.0.256.1
  Locale ID:	1033

Additional information about the problem:
  BCCode:	1a
  BCP1:	0000000000000031
  BCP2:	FFFFFA8006308410
  BCP3:	FFFFF88000BD7000
  BCP4:	FFFFF8A001A342B6
  OS Version:	6_1_7600
  Service Pack:	0_0
  Product:	256_1

This BSOD says there's a problem with ntsf.sys

Code:

Problem signature:
  Problem Event Name:	BlueScreen
  OS Version:	6.1.7600.2.0.0.256.1
  Locale ID:	1033

Additional information about the problem:
  BCCode:	24
  BCP1:	00000000001904FB
  BCP2:	FFFFF88007C58A78
  BCP3:	FFFFF88007C582D0
  BCP4:	FFFFF88001319173
  OS Version:	6_1_7600
  Service Pack:	0_0
  Product:	256_1

While looking at the text document I have with these things in it, I noticed that the additional codes were different for each instance of the BSOD. I won't post those unless that becomes necessary though.