OK, as you have said its a desktop, lets assume it is.
CPU speed? If its much below 300mhz, you may have a problem.. although.. my old machine was a P166 32mb which burnt CD's OK (providing you didnt exceed 2X speed!) AND ran Norton Internet Security and AntiVirus.
Unless your machine is really slow, it shouldnt have a problem with AV or firewall software.. try the software suppliers website for suggestions.
RAM is cheap, it might be an option to look at.. as you have a branded machine, try Kingston or Crucial, they should be able to match memory to your PC.
As writers are also cheap now (even external), upgrade would be cheaper, however in the longer term, if you have a decent monitor and can afford around £500 to £600, this should kit you out with a capable system with an internal CD writer and plenty of RAM.
Cheers
Tim