Safe Mode simply starts the PC is reduced functionality without loading all system and device drivers.
PCs are not like cars whereby components, over time suffer from wear and tear. They either work or they don't. Memory , CPU , Hard Disk etc wont wear out as such. They will , eventually fail. As will any mechanical or electrical device but that failure is permanent. Memory may develop faults, Vista & 7 have a memory diagnostic or you can try memtest x86 which is a pretty good indicator if your RAM is still okay. The Power Cut hasn't affected you as your PC boots, but you could test your PSU (Power Supply Unit) with a tester, these cost no more than a tenner from any local PC retailer. Probably cost more than Tevez if you go to Maplin.
Is there any hope? Yes, if your components check out, and it's software based errors, slow etc then a reinstallation of Windows will return the PC back to day one. If you go down that route ensure all data is backed up although 7 & Vista back up to Windows.old if you reinstall without formatting the disk. You will also need to reinstall all software; printer , drivers, Anti Virus, Office etc so make sure you have all your licences to hand first.
If reinstall isn't an option , and the components check out you will probably need someone that knows what they are doing to look at it and so what maintenance or tweaks can be done. Or if it needs more RAM. Usually though 'the kid next door' is not the best option and causes more harm than good. Someone who really knows what they are doing is best loooking at it.