I also have Windows 7, and it's 64-bit, and I've got 8GB of RAM. I found no problems installing FSX Gold (which is the "full enchilada" incl the Acceleration Pack). I had no probs installing and running the sim. The only problem you WILL face on Win 7 is adding in scenery, as there is a glitch in the way that Win 7 handles the file selection process (but there is another thread somewhere on the forums and elsewhere that deals with this).
I echo HueyTeam's recommendation not to install FSX on C drive, but only if you are prepared to purchase and install a 2nd hard drive. Some people believe strongly in partitioning hard drives (where a "pretend" division makes a single physical hard drive into 2 or more virtual hard drives) - however, this is false economy in terms of performance, as the hard drive heads have to buzz back and forth between the 2 divisions if you have the system on 1 and FSX on the other, thereby slowing things down and wearing out your hard drive. You'd only need a 250GB hard drive as a 2nd drive, but since you might end up with heaps of add-ons and things, it's probably better (and certainly from a cache-size point of view - try to get a drive with a 64MB cache) to get a 500GB for your 2nd drive. I've actually got 3 physical hard drives: C for Windows and various programs, D for FSX, and E for the Windows virtual memory (paging) file. From my experience, this gives optimal performance, and also makes defragmenting more efficient, effective and faster (esp if you set the size of the paging file manually with a min / max size - in your case, 6144 as min, max 9216).
Are you using an Antivirus like Norton, McAfee or Trend Micro? If yes, I would put money on part of the installation process being "blocked" by over-zealous default settings by one of those 3. I do not put any stock at all in the "swiss army knife" approach to security that the 3 big players (and many others) take - it's just a recipe for intrusiveness, more CPU overhead, and a nice big single juicy target to enable a virus to take out ALL security on a PC in 1 fell swoop: I believe (and practice) in defense in depth and variety!
But in terms of the actual problem you are having (and none of the above will actually fix that, BTW), it sounds more like you have one of the following problems:
1) A virus or spyware.
2) Windows Registry errors.
3) Hard drive corruption.
4) Unstable device drivers.
You could fart around for some time tracking each of these down. If your PC is not your "do everything PC" (with emails, photos et al on it), I'd "nuke" it back to default (however you achieve that) and start again - that will take care of at least 1 & 2, prob 4, maybe 3.
Otherwise, you're going to need to address those 1 at a time. I'd start with the easiest - #3. You'll need to run CHKDSK and make it look for bad sectors. Let us know if you need instructions on that. Once that's done - and it will take a long time on a 1TB drive - poss a couple of hours, you will need to do a darn good defrag. The Windows defragger is pretty hopeless - I use Perfect Disk (a brilliant piece of software, but costs USD$50 or thereabouts), but for my customers who don't want to pay I install MyDefrag (available for free from
www.filehippo.com). You will need to run that using the System Disk Monthly setting. It will take quite a while (depending on the amount of stuff you have already on the hard drive), but is the next best defragger after Perfect Disk (and I've tried a few defraggers, believe me!).
If it's #1, you'll need a good AV (I recommend Avast as it can do a boot-time scan) to look for viruses, and some good antispyware progs to check for other greeblies. I specialise in this sort of hunting, and it's very hard to actually explain the ins & outs easily. But suffice to say I do "aggressive" scans using Spybot, Super Antispyware and Malwarebytes' Anti-Malware. All of those progs have the ability to also be "intrusive", plus can have trouble running under Vista or 7 if they aren't installed / configured properly - this is not a fault of theirs per se, but most people don't understand how to set up software full stop, and this is problematic. At the very least, you will need to be aware of how to change security permissions, especially for Spybot.
If it's #2 (and I would look at that anyway), you'll need a good Registry cleaner. There is a lot of debate as to the rightness or wrongness of using Registry cleaners, but I find on balance that it is better to than not. I use 2 payware progs that are excellent - TuneUp Utilities 2010 & PC Tools Registry Mechanic. The TuneUp one is avail as a fully-functional 14-day demo - but as with the antispyware progs, one can end up with it being intrusive using default settings. However, it's Registry Cleaner is very good, so you could install, run the cleaner, then uninstall - that would minimise issues for you. I also use Glarys Utilities (their reg cleaner is pretty good and safe) and the 4.7 version of TweakNow (their new one is not as good, IMHO). I find that no 1 registry cleaner is effective, hence the use of all 4. Sometimes I use the registry cleaner built into CCleaner, but I have seen it cause problems so am somewhat leery of that one.
The hardest one to troubleshoot will be #4. The only thing you can do there is try finding the latest drivers for your video card and motherboard chipset and install those to see if that helps. I use a subscription-based bit of software called DriverAgent to help me update my client's PCs to the very latest / best / stable drivers for ALL hardware components - but this is a very fiddly process that requires fairly expert knowledge (& a reasonably expensive subscription) - but it does yield very good results.
Well, that's a lot for you to consider - I hope there is something useful to you there.