Computer will not boot up. Beeping

Hello,

Sorry this is a long post. I'll try to save people time by giving the short version first. I am having problems rebooting. I can get the fans and lights to come on, but there is a series of long beeps that are ongoing. I thought it was a RAM problem, but it appears that the computer may be destroying my RAM

Here is the long story:
I have a HP pavillion a1450n. Over the last four years, about once per year I go on vacation and leave my house a little bit cooler than normal (about 55 degrees). While I am gone, I have my computer shut down. When I return, I find that the computer won't power up. I usually get it to work by blowing warm air with a blow dryer on it. Over the years I have learned to not turn the machine off.
Well, the other day, I noticed our internet was out. I therefore, went to restart via windows and instead of restarting the computer shut down. Then when I tried to turn it on, I got the similar symptoms that I have had in the past. Absolutely no power (no lights, no fans, no beeps). I therefore tried blowing some warm air on it as usual and no results. I ultimately opened the computer up and cleaned the dust out of it. I also unplugged the RAM and then seated it back firmly.

Eventually, I got the power to come back, but when I did, it wouldn't reboot. Instead, I got a series of constant long beeps. I looked it up on google and saw that this was normally a RAM problem. I have two 1GB DDR ram sticks that are original to the machine. By trial and error, I was able to find that when i used one specific stick it would boot up normally, but if the other one was in, it would not. So, I put the good one in and kept the computer running. When I returned home today, I found that the computer was frozen so I restarted it. When I restarted it, it wouldn't reboot even with the good RAM in it.
I'm wondering if this RAM is now bad too? What could be the problem?

I appreciate any help that I get.

Thank you,
jimmycaps