Lights  1 & 3 is the code for a memory issue. You also need to see if you can determine the sequence of beeps. Then you can go HERE and see if they match any listing. My feeling at this time is the beeps would back up the lights and indicate a memory issue. So two things one is a CMOS reset and the other is memory testing, For memory testing pull all the memory out of the system. Then start by placing one stick into slot #1 which is the slot closest to the processor. See if the system will boot. Then remove that stick and replace it with the next and repeat. Do this for all the Sticks. For a system CMOS reset go HERE and follow the instructions. Note that this will reset your bios to the default conditions so if you have made any changes they will revert back to the default settings.  
I have a 3 year old DELL XPS 400/9150 that has been having some system instability presumably caused by the hard drive that had many bad sectors. With the help of  a co=worker, I replaced the Hard Drive (Western Digital) and got the system to work again with the help of the DELL Recovery CD. The PC worked for a few days and while I was tweaking the drivers for optimum functionnality (using DELL's website), I opted to update the BIOS from version A02 to version A07. For a split of a second, it appeared that the screen displayed "update successful", but a second later, the system started to emit beep codes then stopped working. I can not boot the sytem nor get the monitor to display anything. F2 and F12 keys are not responding. I am not sure if the keyboard is a problem. In short, my computer is not passing the DELL Bios screen at boot-up. Led lights 1 and 3 are lit once the beep codes are emitted. I tried using the floppy drive and the CD/DVD ROM's but no not avail. Does anyone have any idea what, if anything, I can do to get my computer to boot-up? With many thanks.
XPS 400 Diagnostic Lights - System emits beep codes