You didn't mention whether you were running 32-bit or 64-bit Windows 7 but I suppose it's possible that your old Aspire 5742Z laptop doesn't have proper Windows 7 drivers for the card reader. Though if that were the case, I'd expect to see some indication of that in Device Manager... you know, an item in "other devices" with a yellow exclamation mark.
Anyway, in your Windows 7 Device Manager, does your card reader show up properly?
For example, on my own desktop I have a Mitsumi combo-drive, with floppy disk drive as well as two SD card readers (USB interface). And these USB card readers show up in Device manager like this:
Now your Aspire laptop may simply be in need of current Windows 7 drivers. It looks like the SD card reader is from Realtek. I haven't done much research, but it looks like you can get all the Win7 32-bit drivers for that laptop from this particular web site
(I don't vouch for it). They also have a 64-bit version of that page.
Note that there are specifically Realtek drivers for that card reader. Perhaps you should try installing them manually, if they're not already the drivers you see installed from Device Manager.
I've also looked on the ACER site, and they suggest that all drivers for the laptop are pre-packaged into Windows 7 with the exception of the following:
But since you have your laptop up and running, I'm going to guess that these drivers were actually downloaded and installed successfully from the Microsoft Windows Updates catalog site during your Windows 7 install.
I'm just fishing around here, because if it's really hard to figure why this particular piece of hardware on the laptop would cause difficulty, since it appears from the ACER site that Windows 7 is supported for that laptop.
Oddly, the ACER site driver screenshot doesn't even show support for WinXP, so I'm a bit puzzled how this is an "old laptop" that you used to run under WinXP? Or am I not understanding something?
EDIT: Oh... I think you have TWO machines, though your system specs show the Aspire 5742Z laptop, which is what I was thinking you're trying to use now that's causing problems.
Can you please straighten out your specs: do you have TWO machines? And which one is the Windows 7 machine that is causing the problem?