Internet Explorer keeps opening on its own with a bunch of weird websites that I've never visited. I receive messages about Host Processes not working any time my computer goes to sleep, and then I have to disconnect from the internet and reconnect. My computer is pretty old and the virus software is probably not up to date. I would really appreciate some help with this matter. Thanks.

My computer is pretty old and the virus software is probably not up to date.

then up date the virus program , also try ,malwarebytes scanner .free one found here ,
Click Here

If you have an older computer then the keyboaed (I assume) is also Old. Try replacing the Keyboard. You could have some keys bad. Expecially the Enter key and or ALT or CTRL Key

Marty

don't think a bad keyboard is going take Ie to weird web sites

Use an updated AntiVirus to scan and clear the virus from your system.Avast is free and good.
Use Free Malwarebytes Anti-malware to clear Malwares and spy wares.If you have installed any toolbar or extensions to IE ,then uninstall them.