Is it possible my anti virus missed one?

My computer has been crazy lately. Ridiculously slow, streaming video abruptly ends, freezing etc. I ran my Symantec antivirus and while I already have 3 trojans in quarantine, it can't find any new threats. I also ran Spybot S%26D and AdAware for spyware; they found a lot and I deleted them all but my computer's still crap.

I can get Norton antivirus free through rogers, so I decided to install it to see if Symantec missed one, but apparently you can only have one antivirus at a time and Norton would make me uninstall symantec, spybot and adaware. I don't really want to do that.

Basically, is it worth uninstalling all that to see if there really is a virus that Symantec missed? Or is there something else that's slowly killing my computer?

Is it possible my anti virus missed one?virus scanner

Yes it is, this is not to put someone down, but according to many. Norton/Symantec is not that powerful enough to free your computer from various malicious threat. I strongly recommend kaspersky or bitdefender to run on your computer.

Note: avoid running two antivirus program on your computer at the same time.

Is it possible my anti virus missed one?anti virus software

Norton and symantec are just the same. What symantec/norton would detect, it removes but wht it misses it stays in your pc. I suggest you get a really good security software. Kaspersky, Avira, Sophos 7, Nod32 are among the best in anti virus. Spyware doctor, AVG antispyware, a-squared antimalware, counterspy are among the best in anti spyware.
SAD BUT TRUE