someone tried to hack my gmail?

[Mark]

last night google notified me that somebody tried to hack my gmail (and facebook )account from NY (i live in oregon),but didn't specify if they succeeded in getting into it.i only have a Gateway laptop (with norton 360 free trial AV Suite)and smartphone (with AVG Free AV). i use Chrome Browser and my WiFi router has WPA 2 activated. i was worried they may have succeeded in doing so and changed my password, i then a couple hours later just deleted the Gmail account altogether and just set up a new one (but the facebook remains with new password).
i'm concerned that by checking my gmail a malware program/phishing program may have been inserted somewhere in my laptop to steal info(passwords,etc.)
1) i ran 2 'quickscans' and 1 Full System Scan,as well as a redundant Hard drive scan and scanned my facebook wall using the Norton 360, it turned up nothing found other than 4 cookies which it removed. also im not noticing any problems with my laptop. did i do enough to stop this hacker and check my laptop for malware?
2) the next day i get a notification that someone is google searching my name (i'm assuming it's the same person trying to get the new gmail address so they can try again.
what else can i do to protect myself from further hacking attempts? im a student and can't afford to lose my laptop from malware and i can't afford a better AV Suite like Kapersky right now. i never open suspicious unknown e-mails with attachments either. i am new to computers and the web but learn very quickly.
can someone recommend a good Free AV Suite to install once my free trial runs out? any assistance and advice to further actions on my part to stop these hacking attempts would be greatly appreciated, Thank You