First of all, base on your computer skill level , you should have a paid Anti-virus software.
It's really possible for some pro to keep computer clean without AV software,
but seems like you are no that kind.
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Then let me tell you the 'free way'. May AV software get free trial edition maybe like 3 months.
And all the AV are no fully guaranteed totally clean your machine, but they are usually good enough.
do as follow
1st install one free trial AV software(trusted big brand ) in your new machine.
2nd
if data is big and can no use flash drive, pull your old hard drive out,
use some connector one side connect your old hard the other connect to your new machine's usb. that is a useful small should no be higher than $20, possible $5 to$10. you can search 'usb hard drive connector/adapter'. then connect to your new machine , this will be used as mobile hard drive. the AV software may auto scan, if not let it do it. then you are good to go.
if no too big data or u don't want to do that u can use flash drive for many loads, this may be slower if big data
u need to run scan to your flush drive each time you connect to your new machine.
and so much that it is. have fun!
Any question let me know.
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as long as u get the latest AV software updated , run a full scan will be fine.
if the AV is out of payment and can no update or disabled, you can go try free trial as above.
you can put it in both of your PCs
by the way 7 years old machine doesn't mean bad or need to be changed.
a new machine could be retarded in a few minutes if some malware or useless software installed.
i have a laptop bought at 2007 nice maintained both hardware and software , still works fine and performance even better than many new laptops.
you may open a topic on maintaining pc if you like.