In addition to your Panda Internet Security I would do a couple of online anti-virus and anti-spyware scans.

Online anti-virus at

Online anti-spyware at

Delete everything they find.

Does that Panda Internet security include a firewall? If so, confirm it is still on through the Control Panel > Security Center.

About those emails. This is called spam and is inevitable, but is not necessarily related to your slow connection. You need to use 'best practices' regarding email which includes;

1] Do not reply to emails where you do not recognize the sender. If you reply saying you want to 'unsubscribe' then they know this email address is live and active.

2] Do not open emails from unrecognized senders. Opening them can send messages back to the spammers that your email address is live and active.

3] Set up rules in your email software to filter out unwanted mail. Usually Tools > Message Rules, or similar.

4] Do not post your email address in posts or forums on the internet. Spam bots trawl forums looking for unguarded email addresses.

5] ISP's nowadays generally filter out most spam before it gets to your POP server, but not all. Some will still get through.

6] Do not preview emails using the preview pane. Previewing a spam email is the same as opening it and can send that message back.

7] Set up a throwaway email address somewhere for those times where you need to quote an email address, but are unsure if they are going to 'pass it on' to 3rd parties. That way you can ditch that email account when the spam gets too much.

Cool Watch out for email scams, eg someone has $10 million in a Nigerian bank account just waiting for you to help them get it out for 30%. If it sounds too good to be true, then it probably is not true.