Windows 7 Constant Appcrashes with ALL installed programs

Hi guys,

Bit of a weird one here, I recently restored an old Dell Dimension 8250 to run windows 7 pro 32bit. It has 1gb of ram and i've heard its capable enough.
The installation went fine and everything worked for a couple of days, but now any non original programs i install appcrash straight away eg. Firefox, daemon tools, utorrent...the lot!
Control panel wont let me uninstall them so i have to delete their folders and use control panel to remove them from list. Then i reinstall and it will work until a few restarts of the system.

Any idea how to fix this? and better WHY is this happening?

Thanks guys any additional info needed just ask.

Also it used to connect to the wireless but now it only sees my nieghbours networks and not mine which is weird as all other laptops in my house can connect fine?

Thanks for replying,

Programs still crash in safe mode, No error is displayed, but task manager shows the process for a few seconds.
I have no third party antivirus as avast is appcrashing also :P
Event viewer shows the appcrashes i have attached a log for one, they are all very similar and have the same exception code.
SFC said it fixed files, but on restart nothing has changed.
MalwareBytes returned over 100 "viruses" and removed them, those included were the runonce process, all my downloaded exe's and almost everything in my tempory internet folder which seemed unrealistic.
Upon restart and login all that is displayed is an app crash for malwarebytes.
Once i close the malwarebytes crash error explorer is loaded and the system still gives appcrash errors for the programs were malwarebytes has NOT removed thier exe.

I have clean installed before with no change.
Attached is malwarebytes log.

Had ubuntu working fine on this machine but honestly ubuntu is more of a hassle :P

I will reinstall tomorrow and reply with results. I have clean installed before and straight away went to download avast but problem still happened. I will download avast installer on laptop and get it running on PC before bringing it online but im sceptical if that will work.
I'll be back tomorrow night, if this works I owe you big time thanks :)

I had a chat with one of my college lecture he reckons its a faulty hardrive which I believe so i will install an OS on a seperate one i have and see if the system will boot it,
Didn't get a chance tonight but will reinstall if that doesnt work

Also 1GB of ram will work with windows 7 I have seen it been done with this exact machine and it was working fine in the beginning, Its by no means a speed demon but it handles general office tasks which is what i really need it for.
I had XP and Ubuntu on it working fine but I really dont want to go back to either :P
That will be a last resort if I cant fix this.

Finally decided that windows 7 really isn't worth the hassle for just an office machine, Capt your suggestion would probably have worked, but I just put xp back on it. Everythings fine with it (and slightly faster too) sometimes the old os's are the best :P Not gonna mark this as solved because it would just annoy people thanks for your help anyway I had planned to upgrade this machine in the future for light gaming but I just realized the price of RDram ha. thanks everyone for the patience.