Firstly, when you do next get your PC to boot sucessfully I'd back up all your valuable data from the hard drive to some external media such as an external Hard drive or burn a DVD etc. The reason for this suggestion is that what you describe is sometimes associated with faulty operation of the hard disk drive - hence the read error which means there was an error reading from the hard drive.
If it was my PC, I'd leave the RAM alone and after backing everything up, I'd shut it down, unplug it from the mains and inspect its internals for loose cables. If this goes well I'd then get the hard drive manufacturers diagnostic software from their website and run that on it. Assuming it passed, I'd try repairing your operating systems MBR (and how you do that, depends what operating system you have installed) but if that still resulted in the same problems cropping up, I'd use the drive manufacturers utility to zero-fill (wipe) the drive and then reinstall the operating system.
If you are a novice with PCs, all of this might be a bit heavy going for you so you could get a computer shop to fix things but I definitely wouldn't use the repairer that suggested swapping the memory around as that clearly has nothing to do with things (and even if the memory was faulty - which its not, the solution would be to replace it). If you're wondering what may cause this sort of error, improper shutdowns and virus activity are common causes (you do have antivirus software installed don't you?) but it's a good idea to reinstall your O/S and software from scratch every now and again anyway to keep things in order.
If you want to give my latter suggestion a shot (and possibly go on a learning curve at the same time), you'll need to find out your hard disk drive make and model and have all of your operating system and software installation DVDs and CDROMs handy. You'll also need to download the hard disk drive (HDD) utility/tool to match your drive from the manufacturers website and make a bootable floppy/CDROM/USB drive etc to go with it - some utilities do this automatically but with others you make the DOS bootable drive first and then simply add the utility file.
How does that sound?