My printer's memory card slot isn't recognized by my computer. I am running Vista. Can anyone help with this. I contacted the printer's tech support and they tried but said it was a Microsoft problem.

Welcome sannallett,
Sounds like a tech support answer. What is the Brand and Model of the printer?
In Device Manager under your Printer is there a notification sign?

I have checked the device manager list and it is all clear. This is an Epson NX515 and I spent almost an hour with their tech support but they ended up telling me it was a problem with Vista.

Well to be honest I can't find a specific answer to your problem, I looked for your printer on the compatibility list and didn't see it, that doesn't mean it won't work they just don't have it listed.
You might want to try the Microsoft Solution Center Hardware devices not detected or not working
Or keep checking back to see if someone else has an answer for you.

I'm guessing you have already tried the troubleshooting option on the Epson Site,
Epson Stylus NX515, Overview - Technical Support - Epson America, Inc.

Sorry I couldn't be more help.