This can either be a Ram problem or some other hardware malfunction. All you need to do is take your Ram modules apart one by one and then try plug in them back one by one by powering on your PC each time. In this way you will be able to confirm that whether its the ram or any other built in hardware problem. Also check if your motherboard`s backup battery is working fine.

Did you ever find out how to fix this issue? I have the same small inspiron laptop, and yeah, I agree, not worth much, but I would like to fix it. And of it's a matter of just replacing a coin batter then I'll do it. Like you, I purchased a new powersupply because I had no idea when the original one went to. Any idea how to replace the coin battery? Did you haev any luck? Thanks. :)

Thank you very much Dave! I'll keep an eye on the time.

Unplug system remove battery hold power button for 10 seconds. Reinstall battery (make sure you didn't get s bad battery), reseat the RAM, plug in, then try power on. What do you get?

Anyone that has built a computer themselves or experienced a hardware failure will tell you that beeps usually mean something is wrong at the hardware level. A software upgrade, unless it is e a BIOS upgrade, usually doesn't cause the problem.   Early motherboards beeped in a certain pattern for different types of hardware failures but that may not be so true anymore with today's advanced diagnostic devices. You still get beeps, but there is no pattern anymore for different issues.  There is a button cell battery usually a 2032 button cell, like that found in hearing aids that generally is good for about three years; you can buy these at any walgreens, walmart, target etc.  This battery backs up the hardware information that the system accesses at start up (i.e. the CMOS information) it also backs up information such as custom bios settings that you may have made and your clock).  If your clock is always wrong when you cold start from being off and unplugged then there's a chance the battery has died.  Thank goodness the battery is very accessible in this machine, just take off the back cover and it's right there.  On my old 17R you have to pull out all the guts to get to it on the bottom of the motherboard.  Sometimes motherboards may sit on the shelf for awhile before your machine is assembled and the button cell runs all that time thus you get it and it seems to fail way too soon when it really didn't.  When I buy a new motherboard I just go buy fresh batteries before I build to avoid any issues with that coming up.  In some systems a dead battery can indeed cause the machine to fail to start with a beep code.   Beep codes repeat until you turn it off.  If you've had the machine more than a year or two try replacing the battery, it is not a difficult procedure all you have to do is remove a few screws and gently pry off the back using a credit card or plastic pry tool so you don't damage the plastic.   You seem to say this is intermitting, still a good troubleshoot to replace the battery not all manufacturers are good about only using fresh batteries god knows how long they may have sat on the shelf before being installed in your machine. I hope this takes care of your problem.

Pop your service tag into the Dell support site, and you should get manuals and service guides with the tables to decode beeps and light patterns.

According to a general beep code chart that I got from a Dell support person, 5 beeps is 'Realtime Clock Power Fail' and  possible cause is CMOS battery failure.

Yes it was the CMOS battery. Not sure why it failed in just over a year, and it's a pain to get to (13 screews and 4 ribon cables). But the computer is now beep free, thanks for the help.