Lotus Approach is a reasonable database but it isn't really programmable. Rather, it relies on a series of macros to perform anything that isn't in a drop down list of options. Lotus 1, 2, 3 is also an excellent spreadsheet application and for many years it was ahead fo MS Excel. How things change...
It really depends on several factors:
1. How easy do you want your database to be ?
2. Do you want a programmable application ?
3. Would you prefer a point and click approach to your data management ?
4. Are you prepared for a learning curve ?
5. How much do you want to spend ?
Alpha Five click here is about the most capable overall database application I can think of. It has more sample databases, built in query tools and so on than anthying else in the world. It is also very, very programmable with either ActionScript or xBasic (a little like Visual Basic).
FileMaker Pro click here is also an excellent alternative, but in my opinion it is nowhere near as powerful or flexible as Access or Alpha Five, but it is streets ahead of Lotus Approach.
Frankly, Access and Excel are superb programs for managing and analysing information and I rather think you would be better off isolating the problems you have running them and, once you sort those problems out, you can concentrate on using them as they should be used.
Since you already have them it seems pointless thinking of spending anything on other software unless you really want to get into something new.
You could possibly try OpenOffice click here which is free, if very limited by comparison to Access and Excel.
What are the problems you have ?
Perhaps if we tried to iron them out you may find a new lease of life returns to your current software. To be honest you'd have to go a long way and have some very extensive needs to go beyond the capabilities of Access and Excel.