Remove the battery, hard drive, optical drive and memory. Install a known-good memory module. If the system starts up and complains about not finding a boot device, or just displays a blinking hyphen, one of the devices you removed is bad. Put in the battery and see if it continues to run. Shut down the system and reinstall one of the memory modules. Try it again. If it still starts up, shut it down, remove the battery again and put in the other memory module in place of the test unit.
Do the same with the remaining components (shut down and remove the battery before installing each part). Save the hard drive for last so you don't have to worry about messing up the operating system with the forced shutdowns. When the system fails to start, you've found your bad part. (If it won't start with all of the parts removed and test memory installed, the logic board has a failed part on it.)
Sometimes removing and reseating a memory module will fix the problem - that would happen automatically with the procedure I just described. Your User's Manual should have the instructions for replacing memory. I'd give you a download link and page number, but the Samsung support
website says the SCH-R700 is a cell phone. Use the complete model number from the bar code sticker on the bottom.