500 error – will new install over old work

I am considering installing a new wordpress OVER the current installation.

Why? My wordpress site had some malicious files (4) found by my website host, so they had my site redirected until I deleted the files. The 4 files were in mirror & smilies & wlw subdir’s within the images directory in wp-includes subdir of the wordpress site.
I expected to be able to get into my wordpress dashboard, but I get the 500 internal error.

If I install a new wordpress OVER the current installation:
– Will it work?
– Will I retain my old wp database, and will it access it?
– Will I be able to access the pages (with my content) from the previous install? If not, how can I get access to my old pages I designed to get my content.
– IS there be an easier way to get the OLD wordpress site up and running (wordpress in the OLD site was up to date as of a few weeks ago)

I know, I should have backed everything up, but I am new at this, and had not made a current backup. PLUS I found out I have to backup the files, and BACKUP the DATABASE separately. I am working to have that so I hopefully won’t have these issues in the future.